Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

\[\large u \cos x=-2 \int\limits \sin x \cos x dx\]

\[\large m=\cos x\]\[\large -dm=\sin x dx\]

Applying this substitution gives us,\[\large u \cos x=2 \int\limits m dm\]
\[\large u \cos x=m^2+C\]
\[\large u \cos x=\cos^2x+C\]

Answer 7

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

Answer 8

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

Answer 9

heh :D

Answer 10

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

Answer 11

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

Answer 12

:)