# Analytical Solution

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 August 20, 2004, 04:19 Analytical Solution #1 Newbie Guest   Posts: n/a 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!

 August 20, 2004, 05:46 Re: Analytical Solution #2 Tom Guest   Posts: n/a 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.

 August 20, 2004, 18:23 Re: Analytical Solution #3 Mohsen Guest   Posts: n/a 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.

 September 7, 2004, 10:28 driven cavity #4 aswad yusak Guest   Posts: n/a 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.