Need help solving the IVP: y' -y = 10te^(2t) with y(0)=1. I found the integrating factor to be u(t)=e^(-t) and the answer I got: y=10te^(2t)-10e^(2t)+11 but my answer is incorrect. I went over the problem a couple times but can't find my error. Thanks for the help!

Question

tiffany_rhodes · Answer

*I used wolfram alpha to integrate for me because I was being lazy and didn't want to use IBP.

ganeshie8 · Answer

you forgot multiplying 11 by e^t

ganeshie8 · Answer

try
y=10te^(2t)-10e^(2t)+11e^t

tiffany_rhodes · Answer

Okay. I thought you found the solution and then used the initial condition to find the constant?

ganeshie8 · Answer

yes

tiffany_rhodes · Answer

You are correct @ganeshie8

tiffany_rhodes · Answer

but why do I multiply 11 by e^t?

ganeshie8 · Answer

whats ur general solution ?

ganeshie8 · Answer

before finding the constant

tiffany_rhodes · Answer

y=10te^(2t) - 10e^(2t) +C

ganeshie8 · Answer

it should be 

y=10te^(2t)-10e^(2t)+Ce^t

tiffany_rhodes · Answer

Hmm, I see what your saying. When I divided the e^(-t) term over I didn't multiply the constant by e^t

ganeshie8 · Answer

show me ur work so that il be able to pinpoint the error step

tiffany_rhodes · Answer

you're*

ganeshie8 · Answer

yes.. i see you figured it out :)

tiffany_rhodes · Answer

Thanks again for your help :)

ganeshie8 · Answer

yw!

ganeshie8 · Answer

btw you may use wolfram to double check ur IVP solution http://www.wolframalpha.com/input/?i=y%27+-y+%3D+10te%5E%282t%29%2C+y%280%29%3D1