# substitution for differential equation

• May 13th 2008, 04:36 PM
johnnymopo
substitution for differential equation
Thanks to anyone taking a look at this. Maybe I've been at it the homework too long, but I'm having trouble wrapping my mind around a initial value problem.

dy/dt = 2 / (y - t )
y(0) = 1
use substition u = y - t to solve

am I on the right track in thinking y = u + t, and therefore dy/dt = du/dt?

thank you.
• May 13th 2008, 04:57 PM
Krizalid
$u=y-t\implies \frac{du}{dt}=\frac{dy}{dt}-1.$

Now substitute.
• May 13th 2008, 05:29 PM
johnnymopo
Quote:

Originally Posted by Krizalid
$u=y-t\implies \frac{du}{dt}=\frac{dy}{dt}-1.$

Now substitute.

a big long "oooohhhhhh" right. thanks