# Math Help - Reduction of order

1. ## Reduction of order

(t)d^2y/dt^2 - (t+1)dy/dy + y = t^2
y1(t) = e^t y2(t) = t + 1

I have to do this is 2 different methods the first method was using variation of parameters which I could do but then when it came to using reduction of order I kept getting stuck half way.

The first thing i did was let y = ue^t then i differentiated and subbed back intothe equation then it was u absent which let me use p = du/dt and dp/dt = d^2u/dt^2 then i got P = tc/(e^t -t) where c is a constant then i couldnt integrate that to find u.

Rewrite your equation in this form $\displaystyle{\frac{t(y''-y')-(y'-y)}{t^2}=1}$
Then $\displaystyle{\left(\frac{y'-y}{t}\right)'=(t+C)'~\Rightarrow~\frac{y'-y}{t}=t+C~\Rightarrow~y'-y=t^2+Ct}$