Recent content by joob

yah, simplest way to solve it is integration by parts. dont forget to use double angles to get rid of sin^2

The divergence of the curl of ANY vector is =0. You can't find that "vector" without some more information, eg boundary conditions.

Are you sure you wrote the problem out right? both equations are for z?

Sorry, I didnt mean to sound insulting.

youll get a slightly easier integral which you can just take the residue of for the answer

your sub to cos(2x) is fine, and then exp's. what you then want to do is substitute z=e^{2 i \theta} thus dz=2i z d\theta . Your substitution was a little funky. thus cos(2 \theta) = \frac{z+ (1/z)}{2} .

last try... \frac{d}{dt} \left[y(t)e^{-4t} \right]= 9e^{3t} \rightarrow y(t)e^{-4t'} \Big| _0^t= \int^t_0 9e^{3t'}dt'

ok sorry , see if i can get it now... \frac{d}{dt} y(t)e^{-4t}= 9e^{3t} \rightarrow y(t)e^(-4t') \Big^t_0= \int^t_0 9e^{3t'}dt'

hmmm, still haven't gotten the hang of how to type formulas here. Ok let's if I get it right this time... After you set up the problem you actually need to do a full integration on the RHS, and you need to evaluate your LFS at the endpoints of integration... [tex] \frac{d}{dt} y(t)e^{-4t}=...

your on the right track. You have the correct integration factor. [tex] \mu(t)= e^{-4t} [tex]

I agree with DH that 'dsolve' is a good tool to use to solve these diffs on maple. There are also a lot of great tools in maple to simplify answers. If all your getting on maple are big nasty answers, your not using it right. read up on 'simplify' ,'factor', and 'collect', those are the 3 most...

also careful with your results. looks like you missed a couple small details. your integrating factor is actually $e^{-x}$ and you should have the boundaries of the LHS of your equation(unless they're supposed to be =0)