The number of arbitrary constants in the general solution of a differential equation of fourth order 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:

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

[Where C is an arbitrary constant]

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

The general solution of the differential equation $\frac{dy}{dx} = e^{x-y} + x^2e^{-y}$ is equal to:

If the slope of the tangent to the curve $y = y(x)$ at any point $(x, y)$ is $\frac{2x}{y^2}$ and the curve passes through the point $\left(\frac{1}{\sqrt3}, 1\right)$, then equation of curve is

The solution of the differential equation $\log_e\left(\frac{dy}{dx}\right) = 5x + 2y$ is given by