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Old   August 20, 2004, 03:19
Default Analytical Solution
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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

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Old   August 20, 2004, 04:46
Default Re: Analytical Solution
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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.
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Old   August 20, 2004, 17:23
Default Re: Analytical Solution
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the solution to that equation is of the nature:


in which A is a constant determined in terms of lambda. But as Tom says this cannot satisfy the BC you presented.
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Old   September 7, 2004, 09:28
Default driven cavity
aswad yusak
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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.
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