# Variation of Parameters

## Main Question or Discussion Point

Hello,
I'm trying to understand this concept. Jere's the problem i'm doing.
I have to find the general solution for:
y'' + 36y = -4xsin(6x)

So you then solve for your characteristic equation and get lamda = +/- 6
so y1 = e^-6x and y2 = e^6x
You get your matrix for w, w1, and w2.
w = 12
w1 = 4xe^6xsin(6x)
w2 = -4xe^-6xsin(6x)

I have the problem at getting u1 and u2.
u1 = 1/3 the integral of xe^6xsin(6x) dx
u2 = -1/3 the integral of xe^-6xsin(6x) dx

How do you do that integration?

Tom

Related Differential Equations News on Phys.org
Your characteristic equation should be of the form y=Asin6x+Bcos6x since the the squareroot of -36 is 6i and -6i =)

dextercioby