CUET Mathematics 2025 14 May Shift 1 PYQs

Which of the following are first order linear differential equations?

(A) $\frac{dx}{dy} + P_1(y)x = Q_1(y)$ : $P_1(y)$ and $Q_1(y)$ are functions of y or constant functions

(B) $\frac{dy}{dx} + P_2(x)y = Q_2(x)$ : $P_2(x)$ and $Q_2(x)$ are functions of x or constant functions

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

(D) $(1 + x^2)\frac{dy}{dx} - 2xy = x^2 + 3$

Choose the correct answer from the options given below:

Consider the differential equation $xdy = (y + 2x^2)dx$. Then which of the following are TRUE?

(A) It is a homogeneous differential equation.

(B) Product of the order and degree of the differential equation in one.

(C) Integrating factor is x.

(D) General solution of the differential equation is $y = x^3 + Cx$, where C is an arbitary constant.

Choose the correct answer from the options given below:

The solution of the differential equation $xdy - ydx = 0$ represents