In the following differential equation $\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^2 = 2x^2 \log\left(\frac{d^2y}{dx^2}\right)$ order and degree 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:

The particular solution of the differential equation $\frac{dy}{dx} = 8yx$ when $y = 1$ at $x = 0$

General solution of the differential equation $\dfrac{dy}{dx} = e^{ax+by}$ is: (where C is an arbitrary constant)

Solution of the differential equation $\frac{dy}{dx} = x + xy - (1 + y)$ is:

The order and degree of the differential equation $\left[2+\left(\dfrac{dy}{dx}\right)\right]^{5/2}=7\dfrac{d^3y}{dx^3}$ is

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