CUET Mathematics 2025 3 June Shift 2 PYQs

The integrating factor of the differential equation, $x^2 \frac{dy}{dx} + xy = log_e x$ is equal to

For the differential equation $x\frac{dy}{dx} + 3y = x^2\log_e x$, which of the following statements are TRUE?

(A) Product of order and degree is 1

(B) Integrating factor is $x^3$

(C) Integrating factor is $3x$

(D) General solution is $y = \frac{x^3}{36}(6\log_e|x| - 1) + Cx^{-3}$, C is an arbitrary constant.

Choose the correct answer from the options given below:

The differential equation of the family of curves $y = Ae^{\alpha x} + Be^{-\alpha x}$, where $a$ and $\beta$ are arbitrary constants, is