The sum of order and degree of differential equation $2x^2 \cdot \left(\frac{d^2y}{dx^2}\right) - 3 \cdot \left(\frac{dy}{dx}\right)^3 + y = 0$ is

For the differential equation $\frac{\left[1+\left(\frac{dy}{dx}\right)^2\right]^{\frac{3}{2}}}{\frac{d^2y}{dx^2}} = k, k \neq 0$, which one of the following is TRUE ?

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

[Where C is an arbitrary constant]

The general solution of the differential equation $ydx - (x + 2y^2)dy = 0$

Match List - I with List - II. Match the integrating factors :

Choose the correct answer from the options given below :

Match List-I with List-II

Choose the correct answer from the options given below:

The solution of the differential equation $e^{\frac{dy}{dx}} = x+1$; $y(0)=5$ is