Help w/ a Differential Equation

[_brady_]

http://img130.imageshack.us/img130/7955/diffeqmr8.jpg

The form we use is:

y=c1*y1+c2*y2+Y

Where c1 and c2 are constants of integration.

I can find y1 and y2 using the characteristic equation:

y1=e^(3t)
y2=e^-t

Then I find the first and second derivatives of Y, and plug those into the original differential equation to get:

2B-4A-8Bt=-3t

Of course this is where I get stuck...one equation two unknowns, and really no clue where to go from here. So, I'm assuming I'm going about it all wrong.

Thanks in advance for any help.

[bigpooch]

Note that if

2B-4A-(8B)t = (-3)t

is true for all t, then clearly,

(8B) = 3 (or B = 3/8)

and (2B-4A) = 0 (or A = B/2)

and therefore, A = 3/16 and B = 3/8.


Thus, the form of the general solution is

c1(e^-t) + c2(e^(3t)) + (3/16 + (3/8)t)te^(-t)

[_brady_]

Cool, makes sense. Thanks a lot!