Form the differential equation from `y = Ae^(3x) +Be^(-2x)`.

Form the differential equation from y^(2) = 4a (x-a)

Form the differential equation from the following y = e^(x)(A cos 2x + B sin 2x)

Form the differential equation from the following y = e^(-2x)(Ax+B)

Form the differential equation for y=e^(2x)[A cos 3x-B sin 3x]

The differential equation formed if y = (A - Bx ) e^(-2x) is :

Find the differential equation for the following y = e^(3x) (A cos 2x+B sin 2x)

The general solution of the differential equation e^(x) dy + (y e^(x) + 2x)dx = 0 is

Show that each of the following expressions is a solution of the corresponding given differential equation. (ii) y=ae^(x)+be^(-x); y''-y=0

Consider the differential equation (dy)/(dx)=e^(x-y+)x^(2)e^(-y) i . Express the equation in the form f(x)dx=g(y)dy. ii . Hence solve the equation.