# Second Order Inhomogeneous ODEs

1. Apr 23, 2010

### vj9

Hello All,

Using the complementary function and particular integral method, find the solution of the diffential equation which satisfies y(0) = 1 and y'(0) = 0.

y'' + 3y' + 2y = 20cos2x

and then can you help about how to check the answer using technology.

2. Apr 23, 2010

### vin300

D^2 + 3D +2=0
c1e^(-x) +c2e^(-2x) +(3sin2x -cos2x)/10
c1+c2-0.1=1
-c1-2c2 +6=0
c2=4.9, c1=-3.8

3. Apr 24, 2010

### vj9

Can you be more specific . I tried to solve the way u suggested but i am stuck.

Many Thanks,
Vj9

4. Apr 24, 2010

### HallsofIvy

First he found the characteristic equation for the homogeneous equation, $D^2+ 3D+ 2= (D+ 1)(D+ 2)= 0$ so that D= -1 and -2 and the "complementary solution" is $C_1e^{-x}+ C_2e^{-2x}$.

Since the right hand side is 20cos(2x), you look for a specific solution of the form Acos(2x)+ B sin(2x). Put that into the equation and solve for A and B.