# Differential Equation help!

• October 21st 2008, 10:52 PM
falconed
Differential Equation help!
I'm having a real hard time solving this:

$dy/dx -5y = 20cos(5x)$

I have tried mixing everything around and I can't seem to remember how to get y and dy, x and dx on separate sides of the equation. I know I am missing one step!

Any help would be great!
Cheers.
• October 21st 2008, 11:00 PM
Chris L T521
Quote:

Originally Posted by falconed
I'm having a real hard time solving this:

$dy/dx -5y = 20cos(5x)$

I have tried mixing everything around and I can't seem to remember how to get y and dy, x and dx on separate sides of the equation. I know I am missing one step!

Any help would be great!
Cheers.

Do you know anything about the integrating factor? This is a scenario where it's applicable. For a little info on the integrating factor, see post #2 of my differential equations tutorial.

--Chris
• October 21st 2008, 11:22 PM
falconed
Quote:

Originally Posted by Chris L T521
Do you know anything about the integrating factor? This is a scenario where it's applicable. For a little info on the integrating factor, see post #2 of my differential equations tutorial.

--Chris

Yeah I do but the example I have in my lecture notes is quite different.

Would I(x) here be e^(5x) or e^(-5x)? Does it matter?
• October 22nd 2008, 08:22 AM
Chris L T521
Quote:

Originally Posted by falconed
Yeah I do but the example I have in my lecture notes is quite different.

Would I(x) here be e^(5x) or e^(-5x)? Does it matter?

It does matter. The integrating factor would be $\varrho(x)=e^{\int -5\,dx}=e^{-5x}$

--Chris