The general solution of the differential equation $ydx - (x + 2y^2)dy = 0$

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

The solution of the differential equation $\dfrac{dy}{dx} = 2^{x+y}$ is

In the following differential equation $\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^2 = 2x^2 \log\left(\frac{d^2y}{dx^2}\right)$ order and degree is:

Match List-I with List-II

Choose the correct answer from the options given below:

The general solution of the differential equation $x^2\dfrac{dy}{dx} + y^2 = xy$ is: (take $\log_e x = \log x$)

Choose the correct statements:

A. The order and degree (if defined) of a differential equation are always positive integrals

B. The order of a differential equation is the highest order derivative of the dependent variable with respect to the independent variable involved in a differential equation

C. If $\frac{dy}{dx} + P(x)y = Q(x)$ then Integrating factor $= e^{\int P(x)dx}$

D. The sum of order and degree of differential equation $1 + (y'')^5 = (y''')^3$ is $8$

E. If the solution of a differential equation of order $n$, contains $n$ arbitrary constant, then it is called a general solution

Choose the correct answer from the options given below: