The solution of the initial value problem $x\frac{dy}{dx} = 2, y(1) = 2$ is

If m and n are respectively the order and degree of the differential equation $(\frac{d^2y}{dx^2})^{2} + (\frac{dy}{dx})^3 + y= 4x$, then the value of $m + n$ is:

The solution of the differential equation $\frac{dy}{dx} + y = 1, y(1) = 0$ is

The order and degree of the differential equation $\dfrac{d^3y}{dx^3} + \left(\dfrac{d^2y}{dx^2}\right)^2 + e^{\frac{dy}{dx}} = 2$ is

If the order and the degree of the differential equation $\left(\frac{dy}{dx}\right)^{\frac{1}{2}} = \left(\frac{d^2y}{dx^2}\right)^{\frac{1}{5}}$ are O and S respectively, then $S - O$ is equal to

In the context of differential equation

Match List I with List II

Choose the correct answer from the options given below:

Integrating factor of the differential equation $(1 - y^2)\frac{dx}{dy} + xy = ay$ is :