# Help with solving a IH equation

1. Oct 24, 2009

### imperiale

1. The problem statement, all variables and given/known data

d2i/dt2 + 6di/dt + 25i = -292sin4t

2. Relevant equations

3. The attempt at a solution

i got a solution of
Ae^(-3t)cos4t + Be^(-3t)sin4t + 292/9(cos4t) + 146/9(sin4t)
want to know if im right

Last edited: Oct 24, 2009
2. Oct 24, 2009

### Staff: Mentor

Your solution looks reasonable. Your solution can be divided into two parts: the solution to the homogeneous equation i'' + 6i' + 25i = 0, and the particular solution to the nonhomogeneous equation you have.

So your general solution is i(t) = ih(t) + ip(t), where ih(t) consists of the first two terms of your solution, and ip(t) consists of the last two terms.

Your homogeneous solution checks with what I got. To confirm that your general solution is correct, all you need to do is check that your particular solution actually works.

From ip(t) = (292/9)cos4t + (146/9)sin4t, calculate ip' and ip''. If ip'' + 6ip' + 25ip equals -292sin4t, your solution is correct.