hey there i need some here
how to solve this
Zxx-2Zxy+Zyy=(e^2x)cosy
it's PDE
i need steps to solve it especially the homogeneous part
thanx

Question

hey there i need some here
how to solve this 
Zxx-2Zxy+Zyy=(e^2x)cosy 
it's PDE 
i need steps to solve it especially  the homogeneous part
thanx

anonymous · Answer

$$_{Zxx} - _{2Zxy}+_{Zyy}=\exp \left( 2x \right) \cos y$$

experimentx · Answer

just a guess
looks like x^2 - 2xy + y^2 --- for homogeneous part

experimentx · Answer

sorry ... i would like to correct that as 
x^2 - 4xy + y^2

anonymous · Answer

will it's a second order PDE 
i have the final solution it's : $$Z _{h}= f(x+y) +xf(x+y)$$
but how to get there, that's what i need to know
thanx for trying anyway ;)

experimentx · Answer

I've very little experience with PDE
what is f(x+y)=?
also the above seems to fit in PDE homogeneous part

anonymous · Answer

well tht's a part of what i didn't understand, i know f(x,y) , f is a function of x and y but this i havnt seen before

anonymous · Answer

:(

experimentx · Answer

stay tuned ... it's a good change for me to review ...
i'll try to reply in few hrs

anonymous · Answer

what if the answer was really in f(x,y) instead of f(x+y) would it be possible to find the solution 
jst with a probability of a typing mistake in the note book i have lool ^_^

anonymous · Answer

any progress?