The sum of the order and degree of the differential equation representing the family of curves $y = mx + m^4$, where m is arbitrary constant, is

General solution of the differential equation $\dfrac{3ydx - 2xdy}{y} = 0$ is :

[where $c$ is an arbitrary constant]

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

The general solution of the differential equation $\log_e\left(\frac{dy}{dx}\right) = ax + by$ is

If $m$ and $n$ are respectively order and degree of the differential equation

$\left(\dfrac{d^2y}{dx^2}\right)^5 + 6\cdot\dfrac{\left(\dfrac{d^2y}{dx^2}\right)^3}{\dfrac{d^3y}{dx^3}} + \dfrac{d^3y}{dx^3} = x^2+5$ then :

The particular solution of the differential equation x(1 + y²)dx - y(1 + x²)dy = 0, y(0) = 1, is:

The solution of the differential equation $\frac{dy}{dx} = \frac{6}{x^2}$; $y(1) = 3$ is :