Hi, Everyone

Can anyone tell me if there is a analytical solution for the equation as follow:

d2u/dx2(two times derivative of x)+lamda(constant)*x2(square of x)*exp(u)=0

The bounary condition is :u(0)=u(1)=0

Thanks!

It's highly unlikely that there is an analytic solution to the equation. I suspect the only (obvious) solution to the equation is

u = -4log(x), lambda=-4,

and this cannot be adjusted to satisfy the boundary conditions.

the solution to that equation is of the nature:

u=A*exp(-x^2)

in which A is a constant determined in terms of lambda. But as Tom says this cannot satisfy the BC you presented.

i want to know, how to use analytical solution in my problem.I'm a final year student now doing my thesis.My thesis is 'driven cavity with aspect ratio 0.25'. I hope you can give me some idea to start my thesis.