Method Of Variation Of Parameter

Method of Variation of Parameter:

This method is very useful in finding the general solution of the second order equation.

The complementary function of (1)

C.F = c₁f₁ c₂f₂

Where c₁,c₂ are constant and f₁ and f₂ are function of x.

Then, P.I = Pf₁ Qf₂

P =

Q =

∴ y = c₁f₁ c₂f₂ P.I

1. Solve (D² 4)y = sec2x

Solution: The A.E is m² 4 = 0

                                m = ±2i

C.F = C₁cos2x C₂sin2x

           P =