# Diff

• May 12th 2008, 11:59 AM
Diff
need help solving this diff plz

3y´ - y = 5x
• May 12th 2008, 12:16 PM
nugiboy
I may be wrong, but i don't think you can solve that because there is only one equation and two unknowns.
• May 12th 2008, 12:40 PM
Moo
Quote:

Originally Posted by nugiboy
I may be wrong, but i don't think you can solve that because there is only one equation and two unknowns.

It's a differential equation :)

y is a function of x
• May 12th 2008, 12:50 PM
nugiboy
Quote:

Originally Posted by Moo
It's a differential equation :)

y is a function of x

How do you do it then lol?
• May 13th 2008, 10:06 AM
Hello again, yes I know its a diff equation but I would need some guidence and help solving it =).

thank you
• May 13th 2008, 11:19 AM
topsquark
Quote:

need help solving this diff plz

3y´ - y = 5x

You can use an integrating factor:

First
$\displaystyle y' - \frac{1}{3}y = \frac{5}{3}x$

Then
$\displaystyle M(x) = e^{\int(-dx/3)} = e^{-x/3}$

So
$\displaystyle e^{-x/3}y' - \frac{1}{3}e^{-x/3}y = \frac{5}{3}xe^{-x/3}$

Notice that the left hand side of the equation is a "perfect derivative"
$\displaystyle \frac{d}{dx} \left ( e^{-x/3}y \right ) = \frac{5}{3}xe^{-x/3}$

$\displaystyle e^{-x/3}y = \int \frac{5}{3}xe^{-x/3}~dx$

I'll let you finish out from there.

-Dan