solve this DE: y' - y = e^x

Question

turingtest · Answer

do you know what an integrating factor is?

anonymous · Answer

no.

anonymous · Answer

I'm so poor at spotting which method to use. :(

turingtest · Answer

If you don't know anything about linear DE's or integrating factors I can't explain the whole idea in two seconds. I suggest you read this. http://tutorial.math.hlamar.edu/Classes/DE/Linear.aspx You can spot the metod because this DE is linear

anonymous · Answer

I know what a DE is, been solving questions all day. How do I separate x's and y's so I can integrate them?

turingtest · Answer

you don't, it's not separable. It's a different form$$y'+p(x)y=q(x)$$which is called a $linear$ DE and is solved with an integrating factor.

anonymous · Answer

With this one your not trying to seperate the x's and y's you want it in the form of$$\frac{dy}{dx} + g(x)y = h(x)$$

anonymous · Answer

lol sorry ill get out of the way :P

turingtest · Answer

haha, no it's fine

anonymous · Answer

turingtest · Answer

for$$y'+p(x)y=q(x)$$the integrating factor is$$\Large e^{\int p(x)dx}$$so what is it in your case

anonymous · Answer

thanks.