Question: Nonlinear 2nd order ode - contd..

Hi,

Thanks a lot for your inputs and help to my previous post. Being novice, I learnt a lot from your inputs.

I am trying to solve a new nonlinear ode problem with the following boundary conditions bcs1 and bcs2 saperately:

a:= -1.24:

slope:= 1: # slope is varying with L

ode:= diff(y(x),x$2) –a*y(x) + y(x)^3 - y(x)^5  = 0

bcs1:= D(y)(0) = 0,   D(y)(L) = slope;

bcs2:= D(y)(0) = 0,   y(L) = 0;

The ode is defined in one dimensional coordinate system. The length is defined by ‘x’. The ode is solved for different lengths values ‘L’ and plotted as variation of y(x) with ‘x’. The attached figure is an expected jpg of the results. (figure is not to scale, its just schematic)

I am getting a trivial solution y(x) = 0 for the above bcs. Would you please suggest me some way to solve this ode, with two boundary conditions bcs1 and bcs2 saperately to get the non-trivial result?

Thanks in advance,

rpd