CUET Mathematics 2026 31st May Shift 2 PYQs

Which of the following are linear first order differential equations?

(A) $\frac{dy}{dx} + P(x)y = Q(x)$

(B) $\frac{dx}{dy} + P(y)x = Q(y)$

(C) $(x - y)\frac{dy}{dx} = x + 2y$

(D) $(1 + x^2)\frac{dy}{dx} + 2xy = 2$

Choose the correct answer from the options given below:

For the differential equation $ydx - (x + 3y^2)dy = 0$, 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:

The solution of the differential equation $(x+1)\frac{dy}{dx} = 1 + y$ is