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

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

If $U(x) = x + \sqrt{1 + x^2}$, then solution of the differential equation $\frac{dy}{dx} + \sqrt{\frac{1 + y^2}{1 + x^2}} = 0$, is :

Match List-I with List-II

Choose the correct answer from the options given below:

General solution of the differential equation $(e^x + e^{-x})dy = (3e^{2x} + 3e^{4x})dx$ is:

[Where C is an arbitrary constant]

The solution of the differential equation $\log_e\left(\frac{dy}{dx}\right) = 5x + 2y$ is given by

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

[where $c$ is an arbitrary constant]