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

The product of order and degree of the differential equation $\left(\frac{d^3y}{dx^3}\right)^2 + x^2y\left(\frac{d^2y}{dx^2}\right)^3 = 2x^5$ is:

For the differential equation $\frac{\left[1+\left(\frac{dy}{dx}\right)^2\right]^{\frac{3}{2}}}{\frac{d^2y}{dx^2}} = k, k \neq 0$, which one of the following is TRUE ?

The integrating factor of the differential equation $x\frac{dy}{dx} - y = 2x^2$ is :

The solution of the differential equation $\frac{dy}{dx} = \frac{x+y}{x-y}$ is

The general solution of the differintial equation : $x\frac{dy}{dx}-ay=1(a\neq0)$ is

The differential equation whose solution is $Ax^2 + By^2 = 1$ where A and B are arbitrary constant is of :

(A) first order and first degree

(B) second order and first degree

(C) second order and second degree

(D) second order

Choose the correct answer from the options given below :