The general solution of $\frac{dy}{dx} = 1 + x^2 + y^2 + x^2y^2$ is:

(given that $C$ is the constant of integration)

If $\dfrac{dy}{dx} = e^{x-y} + x^2e^{-y}$, then the solution of the differential equation will be:-

Match List-I with List-II

Choose the correct answer from the options given below:

The substitution $y=vx$ transforms the differential equation $xdy-ydx=\sqrt{x^2+y^2}dx$ into

The solution of the differential equation $\frac{dy}{dx} = \frac{6}{x^2}$; $y(1) = 3$ is :

The differential equation $\frac{dy}{dx} + \frac{x}{y} = 0$, represents the family of curves:

The differential equation representing the family of curves $y = Ax + \frac{B}{x}$, $x \neq 0$ where A and B are arbitrary constants, is given by