CUET Mathematics 2026 29th May Shift 2 PYQs

The general solution of the given differential equation $dy + (2y - e^{-2x})dx = 0$, is:

[where c is an arbitrary constant]

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:

The general solution of the differential equation $\frac{xdy}{dx} + 4y = x^3, (x \neq 0)$ is: