(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Ive been working on this problem for way too long and i can get it almost right except im missing a factor of (1/12)e^4x and for the life of me i cant figure out why. Ive been mostly trying to use the methode of undeermined coefficients to no luck and so have also tried variation of parameters and still something is not going right. I have run the equation through my 89 and i have the answer i just cant seem to get it by hand.

2. Relevant equations

y''-2y'-8y=3*e^(4x)-5x^2

complimentary solution=yc=C1*e^(4x)+C28*e^(-2x)

as for finding the particular solution(yp) i think this is where my problem is.

the actual solution as given by my ti 89 is y=((x/2)

+C1-(1/12))*e^(4x)+C2*e^(-2x)+(5x^2)/8-(5x)/16+15/64

3. The attempt at a solution

using yp=Axe^(4x) +Bx^2+Cx+d i got it all right except that im missing the (1/12)*e^4x value and ive tried to many varriations to list them all here but i have litterally spent hours on this and i probally should have posted this back when i was still at only 3 hours worth of time into it but im well beyond that now and its time for a little rest so i can wake up and keep hammering at this one till i get it.

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# Method od undetermined coeff help needed.

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