Solving y' - ytan(x) = 2sin(x): What Went Wrong with My Integrating Factor?

[okhjonas]

Hello, I've got a problem with a differential equation...

Homework Statement

y' - ytan(x) = 2sin(x)

The Attempt at a Solution

I've tried to multiply the equation with the integrating factor $$e^{-\frac{1}{cos^{2}x}}$$ and then express the equation as $$ye^{-\frac{1}{cos^{2}x}}=\int2sin(x)e^{-\frac{1}{cos^{2}x}}dx$$ but then I've got lost..

(excuse my bad English)..

 

[tiny-tim]

Hello, I've got a problem with a differential equation...

Homework Statement

y' - ytan(x) = 2sin(x)

The Attempt at a Solution

I've tried to multiply the equation with the integrating factor $$e^{-\frac{1}{cos^{2}x}}$$ and then express the equation as $$ye^{-\frac{1}{cos^{2}x}}=\int2sin(x)e^{-\frac{1}{cos^{2}x}}dx$$ but then I've got lost..

(excuse my bad English)..

Hi okhjonas!

hmm … I thought you'd got some sleep?

No, your integrating factor is wrong …

you need an f with f'/f = - tanx …

oh I see … you differentiated tanx … try integrating it!