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, $x\frac{dy}{dx} = y(log_e y - log_e x + 1)$, then which of the following are true?

(A) It is a linear differential equation

(B) It is a homogenous differential equation

(C) Its general solution is $log_e\left(\frac{y}{x}\right) = Cx$, where C is constant of integration

(D) Its general solution is $log_e\left(\frac{x}{y}\right) = Cy$, where C is constant of integration

(E) If $y(1) = 1$, then its particular solution is $y = x$

Choose the correct answer from the options given below:

For $y \neq 0$, the particular solution of the differential equation $2ye^{xy}dx + (y - 2xe^{xy})dy = 0$ at the point (1, 1) is