show that y=e^-t is a solution of d^2y/dt^2-dy/dt - 2y=0.

find the values of m for which y=e^mt is a solution of d^2y/dt^2+dy/dt -6y=0.

find the solution of the first order initial- value problem dy/dx=2x. y(1)=2.

Solve the initia-value problem d^2y/dx^2+ dy/dx = e^x y(0) = 1, y (0)=0.