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

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

General solution of the differential equation $\dfrac{dy}{dx} = e^{ax+by}$ is: (where C is an arbitrary constant)

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

The general solution of the differential equation $\frac{dy}{dx} + y\cot x = 2\cos x$ is (Where C is an arbitrary constant)

The solution of the differential equation $log_e\left(\frac{dy}{dx}\right) = 3x + 4y$ is given by

Particular solution of the differential equation $dy + 2xy^2 dx = 0$, given that $y=1$, when $x=0$, is

The differential equation whose solution is $Ax^2 + By^2 = 1$ where A and B are arbitrary constant is of :

(A) first order and first degree

(B) second order and first degree

(C) second order and second degree

(D) second order

Choose the correct answer from the options given below :