Match List I with List II.

List I	List II
A. $\frac{d^2y}{dx^2} + \frac{dy}{dx} = 0$	I. order 3, degree 1
B. $\left(\frac{d^2y}{dx^2}\right)^2 = 0$	II. order 2, degree 2
C. $\frac{d^3y}{dx^3} + \frac{d^2y}{dx^2} + y = 0$	III. order 2, degree 1
D. $\sin\left(\frac{dy}{dx}\right) + 5y = 0$	IV. order 1, degree is not defined

Choose the correct answer from the options given below:

The solution of the differential equation $x\frac{dy}{dx} = 2x^2 + 1$; $x \neq 0$ with $y = 1$ when $x = 1$, is

The solution of the differentiable equation $2x\frac{dy}{dx} + y = 14x^3, x > 0$, is

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

The sum of the order and degree of the differential equation: $\left(x + \frac{dy}{dx}\right)^2 = \frac{dy}{dx} + 1$ is

If m and n are the order and degree of the differential equation $9\frac{d^3y}{dx^3} = \left\{1 + \left(\frac{dy}{dx}\right)^2\right\}^{5/2}$, then the value of $2m+3n$ is equal to

Let the degree and order of the differential equation $2x^3\frac{dy}{dx}-5\left(\frac{d^2y}{dx^2}\right)^2=6\left(\frac{dy}{dx}\right)^3$ be $m$ and $n$ respectively. Then

(A) m = 2

(B) n = 3

(C) m = 3

(D) mn = 4

Choose the correct answer from the options given below: