## hary 2 years ago du(x)/dx- tan(x)u(x)=-2sinx find u(x) inhomogeneous differential equation

1. SithsAndGiggles

$u'-(\tan x)u=-2\sin x\\ (\cos x)u'-(\sin x)u=-2\sin x\cos x$ What can you say about the LHS?

2. zepdrix

I saw you were stuck on this one earlier hary, what was the book answer again?

3. hary

u=cosx +C/cosx this was the book answer

4. zepdrix

Ah ok good. You must've made a small mistake near the end then. Because your integrating factor looked good.

5. hary

hmm im guessing the same too..but couldnt figure out where

6. zepdrix

$\large u \cos x=-2 \int\limits \sin x \cos x dx$ $\large m=\cos x$$\large -dm=\sin x dx$ Applying this substitution gives us,$\large u \cos x=2 \int\limits m dm$ $\large u \cos x=m^2+C$ $\large u \cos x=\cos^2x+C$

7. hary

owh god thats brilliant...did a blunder at my RHS integration

8. myko

lol, what a mistake. Time for me to go to sleep I think

9. zepdrix

heh :D

10. hary

@zepdix thanks alot!!!! was cracking my head on this for quite long...pheww thats a relief... thankx again...

11. hary

@myko thankx to you too...been a great help

12. myko

:)