The DE has the form...
(1)
... and its solution is...
(2)
... where...
(3)
Here we have...
(4)
... so that is...
(5)
The integral in (5) has no elementary approach ...
Kind regards
I'm trying to solve this problem but having some difficulty, could somebody please help me out?
y" + (1+ey)y = 0. Subject to y(0)=1, y'(0)=0
I've used the expansion y(x)=y0(x) + ey1(x) + ...
when i differentiate this twice and substitute into my eqn and collect powers of e i get two equations:
y0" + y0 = 0
y1" + y1 = 0
I think this is wrong and not really sure what to do.
Thanks for any help (and sorry about the poor layout of the problem)
Thank you Danny, that really helped me out a lot!
I'm just having some trouble with this last bit now.
If i have: y1" + y1 = -(cosx)^2
then would the homogeneous solution be cos x? or A + B(e^x)?
and also I'm completely unsure how to find the particular solution
Thank you so much ive got an answer which when i check it it works
y = cos(x) + e( cos(x) - 1/2 - 1/6 cos(2x) )
The only thing is i havent used the initial conditions anywhere other than working out the solution of y0 = cos(x).. do i need them for working out the value of epsilon?