What am I doing wrong? Solving first order DE's

[DWill]

What am I doing wrong?? Solving first order DE's

Homework Statement

Solve the following first order differential equation:
ty' + (t+1)y = t; y(ln 2) = 1, t > 0

Homework Equations

The Attempt at a Solution

I try to solve this using the method of integrating factors. First I divide the equation by t to get:

y' + [(t+1)/t]y = 1

So following from this I find the integrating factor u(t) = t*e^t

So to solve this I just take an integral of both sides of equations to get:

y*t*e^t = e^t(t-1) + C

Is this right? I now just have to solve for y, and then plug in for the initial values to get C. But the answer I get does not match my book's answer! Can anyone show me what I did wrong here? Thanks

 

[Alewhey]

So to solve this I just take an integral of both sides of equations to get:

y*t*e^t = e^t(t-1) + C

Is this right? I now just have to solve for y, and then plug in for the initial values to get C. But the answer I get does not match my book's answer! Can anyone show me what I did wrong here? Thanks

I get the same. What is the book's answer?

 

[DWill]

The book says the answer is:

y = (t - 1 + 2e^(-t)) / t, where t cannot equal 0.