Question

Find the solution of the given IVP. ty' + (t+1)y = t
y(ln8) =1, t>0

Answer 1

The DE looks linear. I'm still confused about the IF though.

Answer 2

it is linear. You could use an integrating factor of \[\mu(t) = e^t t\]

Answer 3

@whpalmer4 So would I get d/dx (te^t)*y = t^2 *e^t ? Then just integrate both sides?

Answer 4

I think you want to divide both sides by \(t\) first, then apply the integrating factor.