The differential equation of the family of curves $y = a \sin(bx + c)$, a and c are parameters, is :

The solution of the differential equation $\dfrac{dy}{dx} = x^2y^2$ with $y = 1$ at $x = 0$ is

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

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

Match List-I with List-II

Choose the correct answer from the options given below:

The sum of order and degree of the differential equation $\frac{\left\{1+\left(\frac{dy}{dx}\right)^2\right\}^{\frac{5}{2}}}{\frac{d^2y}{dx^2}} = p$ is :

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: