Differential Equations Test-2

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CBSE TEST PAPER-02
CLASS - XII MATHEMATICS (Calculus: Differential Equations)
1. Find the order and degree
4
2
2
ds d s
3 0
dt dt
s
? ?
+ =
? ?
? ?
[1]
2. Verity that the function is a solution of the corresponding diff eq.
-1 2 1 2
x + y = tan y ; y y + y + 1 = 0
[1]
3. Form the differential equation representing the family of ellipses having foci on
x – axis and centre at the origin.
[4]
4. Form the diff. eq of the family of circles touching the x – axis at origin. [4]
5. Solve the diff eq.
( )
x x 2
e tan y dx + 1 e Sec y dy = 0 - [4]
6.
Solve Cos
dy
=a, ; y = 1 when x = 0
dx
? ?
? ?
? ?
[4]
7.
Solve.
( )
2 2
x - y dx+2xy dy = 0
[4]
8. Solve
x Cos  + y Sin  y dx = y Sin  - x Cos  x dy
y y y y
x x x x
? ? ? ? ? ? ? ? ? ? ? ?
? ? ? ?
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ? ? ?
[4]
9. Find the particulars solution of diff . equation.
( )
2
1+x 2  dy xy dx Cotx dx + =
[6]
10. Find the particular solution of diff. equation
x Cot x = 0
dy
y x xy
dx
+ - +
[6]
```

## FAQs on Differential Equations Test-2 - Class 12

 1. What are differential equations?
Ans. Differential equations are mathematical equations that involve one or more derivatives of an unknown function. They are used to model various physical and natural phenomena, such as the growth of populations, fluid flow, and electrical circuits.
 2. What is the purpose of studying differential equations?
Ans. Studying differential equations allows us to understand and describe the behavior of systems that change over time. It provides tools to solve problems in physics, engineering, economics, and many other fields by formulating mathematical models and analyzing their solutions.
 3. How are differential equations classified?
Ans. Differential equations can be classified based on their order and linearity. The order refers to the highest derivative present in the equation, while linearity refers to whether or not the equation is a linear combination of the unknown function and its derivatives.
 4. What are the different methods to solve differential equations?
Ans. There are various methods to solve differential equations, including separation of variables, integrating factors, substitution, power series, and Laplace transforms. The choice of method depends on the type and complexity of the equation.
 5. Can differential equations be solved analytically or numerically?
Ans. Differential equations can be solved both analytically and numerically. Analytical solutions involve finding an exact mathematical expression for the unknown function, while numerical solutions use approximation techniques to obtain an approximate solution. Analytical solutions are preferred when possible, but numerical methods are often necessary for complex equations or when an exact solution is not feasible.
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