Differential Equation NAT Level - 2 - Physics MCQ

The correct answer is: 1

This is an example of differential equation reducible to Homogeneous Equations.

Now, put  x + a = e^z.
or   z = log(x + a)
Now,





⇒ λ = 1/3 = 0.333

The correct answer is: -0.333  

Integrating Both sides, we get

Now, it is a Bernoulli's Equation, so we put 

The correct answer is: 2

Let y₁ = e^x and y₂ = x be two solutions of given Differential Equation. Thus,

By the method of variation of parameters

Hence, α = 0.5

The correct answer is: 0.5

Equation of parabola is

y² = x
 

At any point (h, k) on parabola

Equation of tangent
(y – k) = m(x – h)

Hence, order of differential equation = 1.

The correct answer is: 1

Combining both, we get

The correct answer is: 0.2

Dividing complete equation by cos²y, we get.

Put tan y = t

This is Bernoulli’s equations

Now, it is a linear Differential Equation.

∴   f(x) =     
 f(0) = e⁰ = 1
The correct answer is: 1

The correct answer is: 3

Let the I.F be x^myⁿ.

Multiplying Differential Equation by I.F it becomes exact

⇒  

This Differential Equation is Exact.

It is exact

⇒ 

3m - n = - 22
 m + 3n = - 4

m + n = –7 + 1  = –6
The correct answer is: -6

Now, let us put.

Solving above Differential Equation, we get,

Put e^z = t
e^zdz = dt

The correct answer is: 1