Starting with d^2u/dx=du/dy or written u(xx)=u(y)
y>0, 0
u(x,0)=1, u(o,y)=u(a,y)=0
Taking the Laplace transform of u with respect to y gives:
L[u(xx)]=su-1, with the left hand side being just the ordinary differential equation as x is not affected by the Laplace.
The general solution is:
u(x,s) = c(1)e^(xSQRT(s)) + c(2)e^(-xSQRT(s)) + c(3),
which could also be written in terms of cosh and sinh.
How do I find c(3) using the method of undetermined coefficients?
Please try to explain it out. Many of my questions are answered by pulsing brainiacs from another dimension who tend to make succinct responses that they understand but please I am not so smart and have to trudge through step by step. Thanks.
2007-12-07
01:57:13
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2 answers
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asked by
entropic v
3