Match the differential equation (List-I) with its order and degree (List-II)

LIST-I		LIST-II
A. $\dfrac{d^3y}{dx^3} + x^2\left(\dfrac{d^2y}{dx^2}\right) = 0$		I. order =3; degree is not defined
B. $\dfrac{d^3y}{dx^3} + y^2 + e^{\frac{dy}{dx}} = 0$		II. order =3; degree=1
C. $1 - \left(\dfrac{dy}{dx}\right)^2 = \left(a\dfrac{d^2y}{dx^2}\right)^{1/3}$		III. order =2; degree=1
D. $y = x\left(\dfrac{dy}{dx}\right)^3 + \left(\dfrac{d^2y}{dx^2}\right)^4$		IV. order =2; degree=4

Choose the correct answer from the options given below:

Let $y = f(x)$ be the solution curve of the differential equation $\dfrac{dy}{dx} + 2y^2 = 0$ if $f(1) = 1$, then $f(2)$ is equal to

Particular solution of the differential equation $\log\left(\frac{dy}{dx}\right) = x + y$, given that when $x = 0, y = 0$ is:

Solution of the differential equation $\frac{dy}{dx} = x + xy - (1 + y)$ is:

Solution of differential equation $\frac{dy}{dx} = e^{x+y} - xe^y$ is

The particular solution of the differential equation x(1 + y²)dx - y(1 + x²)dy = 0, y(0) = 1, is:

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