Help with solving a IH equation

[imperiale]

Homework Statement

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

Homework Equations

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 I am right

 

[Mark44]

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) = i_h(t) + i_p(t), where i_h(t) consists of the first two terms of your solution, and i_p(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 i_p(t) = (292/9)cos4t + (146/9)sin4t, calculate i_p' and i_p''. If i_p'' + 6i_p' + 25i_p equals -292sin4t, your solution is correct.