CUET Mathematics 2025 26 May Shift 2 PYQs

The degree of the differential equation $\left(2 + \left(\frac{dy}{dx}\right)^2\right)^{\frac{3}{2}} = a^2 \frac{d^2y}{dx^2}$ is:

Given differential equation, (1 + y²)dx = (tan⁻¹y - x)dy, then which of the following is/are true?

(A) Integrating factor = tan⁻¹x

(B) Integrating factor = tan⁻¹y

(C) Integrating factor = e^(tan⁻¹y)

(D) Degree = 1

Choose the correct answer from the options given below:

For the differential equation $y\frac{dx}{dx} - (x + 3y^2)dy = 0$, which of the following statements are true?

(A) It is a linear differential equation

(B) It is a homogenous differential equation

(C) Its general solution is $x = 3y^2 + Cy$ : C is an arbitrary constant

(D) If $y(0) = 1$, then its particular solution is $x = 3y^2 - 1$

Choose the correct answer from the options given below: