Question

find the general solution of the given differential equation.

1. y'' + y = tan t, 0 < t < π/2

2. y'' + 4y' + 4y = t^-2 e^-2t , t > 0

find the solution of the given initial value problem.

3. y'' + y' − 2y = 2t, y(0) = 0, y'(0) = 1

Answer 1

All these problems can be solve by method of variation of parameters.

The general solution is y=C.E+P.I

P.I=P(x)y1(x)+Q(x)y2(x).

Where,