CUET Mathematics 2025 22 May Shift 1 PYQs

For the differential equation $x\frac{dy}{dx} + 2y = x^3\log_e x$

(A) Integrating factor is $2x$

(B) Integrating factor is $x^2$

(C) General Solution is $y = \frac{x^3}{16}(4\log_e|x| - 1) + Cx^{-2}$ Where C is an arbitrary constant.

(D) General Solution is $y = \frac{x^4}{16}(4\log_e|x| - 1) + C$ Where C is an arbitrary constant.

Choose the correct answer from the options given below:

The general solution of differential equation $\frac{dy}{dx} = e^{x+y}$ is

Solution of the differential equation

$\frac{dy}{dx} = \sqrt{1+x^2+y^2+x^2y^2}$ is: (Here C is an arbitrary constant)