# Math Help - Diff

1. ## Diff

need help solving this diff plz

3y´ - y = 5x

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

3. 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

4. Originally Posted by Moo
It's a differential equation

y is a function of x
How do you do it then lol?

5. Hello again, yes I know its a diff equation but I would need some guidence and help solving it =).

thank you

need help solving this diff plz

3y´ - y = 5x
You can use an integrating factor:

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

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

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

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

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

I'll let you finish out from there.

-Dan