CUET Mathematics 2026 18th May Shift 2 PYQs

The integrating factor of the differential equation $(x log_e x)\frac{dy}{dx} + y = 2log_e x$ is

For the differential equation $\left(x \log _{e} x\right) d y=\left(\log _{e} x-y\right) d x$

(A) Degree of the given differential equation is $1$.

(B) It is a homogeneous differential equation.

(C) Solution is $2y \log _{\mathrm{e}} \mathrm{x}+A=\left(\log _{\mathrm{e}} \mathrm{x}\right)^{2}$, where $A$ is an arbitrary constant

(D) Solution is $2 y \log _{e} x+A=\log _{e}\left(\log _{e} x\right)$, where $A$ is an arbitrary constant

Choose the correct answer from the options given below :

Which of the following differential equations are of order 2 and degree 1?

(A). $\frac{d}{dx}\left(\frac{dy}{dx}\right) + x\frac{dy}{dx} = y$

(B). $\frac{d^2y}{dx^2} + x = \sqrt{\frac{dy}{dx} - y}$

(C). $\left(\frac{dy}{dx}\right)^2 + \frac{d^2y}{dx^2} = \log x$

(D). $\left(\frac{dy}{dx}\right)^2 + \frac{dy}{{dx}} = 3$

Choose the correct answer from the options given below: