Question

diff eqns: y=sinxcosx-cosx; y(0)=-1; show y is a soln of y'+tan(x)y'=cos^2(x). where y'=-sin^2(x)+sinx+cos^2(x).

Answer 1

y'+tan(x)y=cos^2(x)
^ is that y supposed to have a ' on it or was that a typo?

Answer 2

yes, both y in the diff eq should have a prime on it.

Answer 3

well either way you just plug in the given solution and check that it is true:
y'+tan(x)y'=cos^2(x)
we are given that
y'=-sin^2(x)+sinx+cos^2(x)
now just sub that into the DE:
-sin^2(x)+sinx+cos^2(x)+tan(x)(-sin^2(x)+sinx+cos^2(x))=cos^2(x)
and check to see if it turns out to be true

Answer 4

yes, i did but couldn't get it to work out. i used various trig ids to try to make it work....but could n't get it

Answer 5

ok let me try...

Answer 6

thank you!!

Answer 7

well...\[-\sin^2x+\sin x+\cos^2x+\tan x(-\sin^2x+\sin x+\cos^2x)\neq\cos^2x\]according to the wolf

Answer 8

http://www.wolframalpha.com/input/?i=simplify+-sin%5E2%28x%29%2Bsinx%2Bcos%5E2%28x%29%2Btan%28x%29%28-sin%5E2%28x%29%2Bsinx%2Bcos%5E2%28x%29%29

Answer 9

huh. ok. well, that makes sense then that i couldnt' get it to work. thank you!!

Answer 10

welcome, good luck finding your typo or whatever :P