Solve the initial value problem dy/dx + 36y = 0 with y(0) = 0 and dy/dx|x=0 = 5

If sin x, cos x, x sin x and x cos x are four possible solutions to a fourth order linear differential equation

calculate the Wronskian and check whether these four solutions are independent

Solve the boundary value problem d2y/dx2 + 2 dy/dx + y = 0 with y(0) = 1, y(log 3) = 2

Solve the initial value problem d3y/dx3 + 6 d2y/dx2 + 9 dy/dx = 0 with y(0) = 0, dy/dx|x=0 = 2, d2y/dx2 |x=0 = 1.

Obtain the exact differential equation for which the solution has the form x2 + y2 = 1. Show that theobtained differential equation is exact.