The solution of differential equation $\sqrt{x+1} - \sqrt{x-1}\frac{dy}{dx} = 0$ is

If the order and degree of the differential equation $\sqrt{\frac{d^2y}{dx^2}} = \left(1 + \frac{dy}{dx}\right)^{\frac{1}{3}}$ are $a$ and $b$ respectively, then the value of $a^2 + b^2$ is

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

Match List-I with List-II

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The degree of the differential equation $\left(1-\left(\frac{d y}{d x}\right)^{2}\right)^{\frac{3}{2}}=k \frac{d^{2} y}{d x^{2}}$ 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:

Which of the following are correct?

(A) The order of the differential equation $\left(\dfrac{dy}{dx}\right)^2+3y^2-5y=0$ is 2.

(B) The degree of the differential equation $x\dfrac{d^2y}{dx^2}=\left(3+2\left(\dfrac{dy}{dx}\right)^2\right)^3$ is 3.

(C) The differential equation representing the curve $y=cx$, $c$ being an arbitrary constant is $ydx-xdy=0$.

(D) The general solution of an ordinary differential equation of $n^{th}$ order contains $n$ independent arbitrary constants.

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