how do you find a particular solution to (15/4)y''-4y'+y=3xe^2x

Question

turingtest · Answer

undetermined coefficients is not too painful

anonymous · Answer

i solved it but got it wrong

turingtest · Answer

our guess will be$$Y_p=(Ax+B)e^{2x}$$$$Y'_p=(2Ax+A+B)e^{2x}$$$$Y''_p=(4Ax+4A+B)e^{2x}$$

anonymous · Answer

can i send you my work so you can see where I went wrong?

turingtest · Answer

ok, but i'm gonna keep going in the meantime

anonymous · Answer

ok

anonymous · Answer

attachment

asnaseer · Answer

TuringTest - your choice of a particular solution is correct, but I think your expressions for the first and second derivatives are wrong.

turingtest · Answer

yes I know I messed up on B
I'm fixing it...

asnaseer · Answer

ok - rilayian I'll leave you in the capable hands of TuringTest :)

anonymous · Answer

ok thanks

anonymous · Answer

I attached my work above and I've looked over it twice and I'm still not seeing where i went wrong'

turingtest · Answer

@asnaseer thanks :D
@rilayian that's kinda difficult to read...

anonymous · Answer

I'll send it again

anonymous · Answer

I'm going to send it on 3 parts

anonymous · Answer

attachment

anonymous · Answer

attachment

turingtest · Answer

you never plugged it into the differential equation!

turingtest · Answer

you have to take your formulas for y, y', and y'' and put them into your problem, then you can solve the system to find A and B

anonymous · Answer

i just realized that lol but even when i did I still got it wrong

turingtest · Answer

your work is fine besides that as far as I can see

anonymous · Answer

i ended up with (33/64)e^2x +(3/8)xe^2x

anonymous · Answer

and it's still wrong

turingtest · Answer

33/64 should be negative

anonymous · Answer

omg thank you soo much!!

turingtest · Answer

should have been$$Y'_p=(2Ax+A+2B)e^{2x}$$$$Y''_p=(4Ax+4A+4B)e^{2x}$$plug it into the equation:$$(4Ax+4A+4B)e^{2x}-\frac{16}{15}(2Ax+A+2B)e^{2x}+\frac{4}{15}(Ax+B)e^{2x}$$and you get for the Ax part$$4Ax-\frac{32}{15}Ax+\frac4{15}Ax=\frac45x$$$$60A-32A+4=12\to A=\frac38$$this is what I had so far, you can finish it out I think if you want

turingtest · Answer

my A is your B

turingtest · Answer

and I already have the coefficient of y'' set to 1, so my way is different

anonymous · Answer

thanks but once I changed it to negative it ended up being correct! thanks soo much

turingtest · Answer

welcome!

anonymous · Answer

:)