Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE) PDF Download

Q1: Which of the following differential equations is/are nonlinear?      (2024)
(a) Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)

(b) Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)
(c) Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)
(d) Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)
Ans: (b, d)

Q2: Consider the functionf(t) = (max(0, t))2 for −∞
ltt
lt
 âˆž, where max⁥(𝑎,𝑏)max(a, b) denotes the maximum of a and bWhich of the following statements is/are true?       (2024)
(a) f(t) is not differentiable.
(b) f(t) is differentiable and its derivative is continuous.
(c) f(t) is differentiable but its derivative is not continuous.
(d) f(t) and its derivative are differentiable.
Ans:
(b)
Sol: Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)∴ f(x) is differential and f′(x) is continuous but f′(x) is not continuous.

Q3: A quadratic function of two variables is given as
Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)

The magnitude of the maximum rate of change of the function at the point (1, 1) is ____(Round off to the nearest integer).      (2023)
(a) 10
(b) 12
(c) 8
(d) 16
Ans
: (a)
Sol: Given :
Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)
Q4: Three points in the x−y plane are (−1, 0.8) (0, 2.2) and (1, 2.8) The value of the slope of the best fit straight line in the least square sense is ___ (Round off to 2 decimal places).       (2023)
(a) 0.25
(b) 0.5
(c) 0.75
(d) 1
Ans:
(d)
Sol: Straight line equation, y = ax + b [Let]
where, a = slope
By lest approximation,
Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)From eqn. (1), we get
Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)⇒ a = 1

Q5: In the following differential equation, the numerically obtained value of y(t), at t = 1, is ___ (Round off to 2 decimal places). 
Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)(2023) 
(a) 0.25
(b) 0.5
(c) 0.75
(d) 0.85
Ans:
(b)
Sol: Given :
Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)We know,
Taylor's series
Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)
Q6: Consider the initial value problem below. The value of y at x = ln 2. (rounded off to 3 decimal places) is ________ . 
(dy/dx) = 2x - y, y(0) = 1      (2020)
(a) 1.386
(b) 0.886
(c) 0.452
(d) 0.642
Ans: 
(b)
Sol: Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)Solution,
Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)
Q7: The partial differential equation Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)is known as      (2019)
(a) heat equation
(b) wave equation
(c) Poisson's equation
(d) Laplace equation
Ans:
(b)

Q8: Consider a system governed by the following equations
Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)The initial conditions are such that Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)Which one of the following is true?       (2018)
(a) Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)

(b) Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)
(c) Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)
(d) Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)
Ans: (c)
Sol: Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)
Q9: Consider the differential equation Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE) There exists a unique solution for this differential equation when t belongs to the interval      (SET-1 (2017))
(a) (-2, 2)
(b) (-10, 10)
(c) (-10, 2)
(d) (0, 10)
Ans:
(a)
Sol: The differentail equation,
Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)Only option (A) not cover 9 and -9. Hence it is correct.

Q10: Let y(x) be the solution of the differential equation Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE) with initial conditions y(0) = 0 and Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE) Then the value of y(1) is _________.        (SET-2 (2016))
(a) 2.50
(b) 5.65
(c) 7.38
(d) 9.36
Ans: (c)
Sol: Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)
Q11: The solution of the differential equation, for Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE) with initial conditions y(0) = 0 and y'(0) = 1, is (u(t) denotes the unit step function),      (SET-2 (2016))
(a) Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)

(b) Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)
(c) Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)
(d) Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)
Ans: (a)
Sol: The differentail equation is
Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)
Q12: A solution of the ordinary differential equation Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)is such that y(0) = 2 and y (1) =Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE) The value of (dy/dt) (0) is _______      (SET-1 (2015))
(a) -1
(b) -8
(c) 3
(d) -3
Ans:
(d)
Sol: Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)
Q13: Consider the differential equation Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE) Which of the following is a solution to this differential equation for x > 0 ?       (SET-2 (2014))
(a) ex
(b) x2
(c) 1/x
(d) In x
Ans:
(c)
Sol: Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)One independent solution is (1/x)
Another independent solution is x.

Q14: The solution for the differential equation Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)with initial conditions x(0) = 1 and Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)      (SET-1 (2014))
(a) t2 + t + 1
(b) sin3t + (1/3)cos3t + (2/3)

(c) (1/3) sin3t + cos3t 
(d) cos3t  + t
Ans: 
(c)
Sol: Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)Auxiliary equation is đ‘š2+9=0m2+9 = 0
Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)
Q15: With initial condition x(1) = 0.5, the solution of the differential equation Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE) is      (2012)
(a) x = t - (1/2)
(b) x = t- (1/2)
(c) x = (t2/2)
(d) x = t/2
Ans:
(d)
Sol: The given differential equation is Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE) with initial condition x(t) = 1/2 which is same as Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE) 
Which is a linear differential equation Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)So, x = (t/2) is the solution.

Q16: With K as a constant, the possible solution for the first order differential equation dy/dx = e-3x is      (2011)
(a) -(1/3)e-3x + K

(b) -(1/3)e3x + K
(c) -(1/3)e-3x + K
(d) -3e-x + K
Ans: (a)
Sol: Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)
Q17: For the differential equation Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)with initial conditions x(0) = 1 and Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)the solution is      (2010)
(a) x(t) = 2e-6t - e-2t

(b) x(t) = 2e-2t - e-4t
(c) x(t) = -e-6t + 2e-4t
(d) x(t) = e-2t - e-4t
Ans: (b)
Sol: Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)
Q18: A differential equation (dx/dt) = e2t u(t), has to be solved using trapezoidal rule of integration with a step size h = 0.01s. Function u(t) indicates a unit step function. If x(0-) = 0, then value of x at t = 0.01s will be given by       (2008)
(a) 0.00099
(b) 0.00495
(c) 0.0099
(d) 0.0198
Ans:
(c)
Sol: Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)
Q19: For the equation Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)  the solution x(t) approaches which of the following values as t â†’ ∞?      (2005)
(a) 0
(b) 5/2
(c) 5
(d) 10
Ans: 
(b)
Sol: Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)
Q20: The solution of the first order differential equation Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE) (2005)
(a) x(t) = x0e-3t

(b) x(t) = x0e-3
(c) x(t) = x0e-t/3
(d) x(t) = x0e-t
Ans: (a)
Sol: Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)

The document Previous Year Questions- Differential Equations | Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course Engineering Mathematics for Electrical Engineering.
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FAQs on Previous Year Questions- Differential Equations - Engineering Mathematics for Electrical Engineering - Electrical Engineering (EE)

1. What are the different methods to solve first-order differential equations?
Ans. Some common methods to solve first-order differential equations include separation of variables, integrating factors, and exact equations.
2. How can we determine the order of a differential equation?
Ans. The order of a differential equation is determined by the highest derivative present in the equation. For example, if the equation contains a second derivative, it is a second-order differential equation.
3. What is the role of initial conditions in solving differential equations?
Ans. Initial conditions are necessary to find a particular solution to a differential equation by providing specific values for the dependent variable and its derivatives at a given point.
4. How do we apply Laplace transforms to solve differential equations?
Ans. By applying Laplace transforms to a differential equation, we can transform it into an algebraic equation, which is easier to solve. After finding the solution in the Laplace domain, we can inverse transform it back to the time domain.
5. Can differential equations be used in electrical engineering applications?
Ans. Yes, differential equations are commonly used in electrical engineering to model circuits, control systems, and other dynamic systems. They help in analyzing and predicting the behavior of electrical systems over time.
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