For the differential equation $x\frac{dy}{dx} + 2y = x^2\log_e x$ (A) Integrating factor is $2x$ (B) Integrating factor is $x^2$ (C) General Solution is $y = \frac{x^2}{16}(4\log_e|x| - 1) + Cx^{-2}$ 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 equation of the curve that passes through $(-1, 1)$ and the slope of line touching to the curve at any point $(x, y)$ is $\frac{3x^2}{y}$, is:

Solution of differential equation $\frac{dy}{dx} = e^{x-y} + 3x^2 e^{-y}$ is:

(where C is an arbitrary constant)

The solution of differential equation $y(1 - x^2)\frac{dy}{dx} = x(1 + y^2)$ is :

The order and degree of differential equation $y = px + \sqrt{a^2p^2 + b^2}, p = \dfrac{dy}{dx}$, $a$ and $b$ are constants are:

If $\dfrac{dy}{dx} = e^{x-y} + x^2e^{-y}$, then the solution of the differential equation will be:-

The differential equation satisfied by the equation $y = ae^{bx}$, where $a$ and $b$ are arbitrary constants, is