Let $y(x)$ be the solution curve of the differential equation

$\frac{dy}{dx} + 2y^2 = 0, y(1) = 1$, then $y\left(\frac{3}{4}\right)$ is equal to:

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

[Where C is an arbitrary constant]

The particular solution of the differential equation $\log\left(\frac{dy}{dx}\right)= 3x + 4y$ satisfying $y = 0$ when $x = 0$ is:

Match List-I with List-II

Choose the correct answer from the options given below:

General solution of the differential equation $(1+x^2)dy + 2xy\,dx = \cot x\,dx$ is:

(where $C$ is an arbitrary constant)

Solution of $\frac{dy}{dx} = (1+x^2)(1+y^2)$ is:

The sum of the order and degree of the differential equation representing the family of curves $y = mx + m^4$, where m is arbitrary constant, is