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Transform differential equation by tranformation rule
*To*: mathgroup at smc.vnet.net
*Subject*: [mg111016] Transform differential equation by tranformation rule
*From*: TrinhDao <hackerdarkrose at yahoo.com>
*Date*: Sat, 17 Jul 2010 08:15:08 -0400 (EDT)
Dear Mathematica users,
I want to transform one different equation (variable r,z) to another
different equation (variable x,y).
The origin equation is :
equation = Derivative[0, 2][u][r, z] + Derivative[1, 0][u][r, z]/r +
Derivative[2, 0][u][r, z] == 0
The transform rule is :
r = Cos[x]Sinh[y]
z = Sin[x] Cosh[y]
============
Now, my task is simple, apply this transform to differential equation.
I do like this :
transformRule = {r[x][y]-> Cos[x]Sinh[y], z[x][y]-> Sin[x] Cosh[y]}
dtrules=Join @@ ({#,D[#,t],D[#,{t,2}]} & /@ transformRule)
But it seems that something is wrong...
=========
And the analytical result is :
anaSolution = 1 / (Sin^2[x] + Sinh^2[y] ) * ( Derivative[2, 0][u][x,y]
+ -Tan[x]*Derivative[1, 0][u][x, y] + Derivative[0, 2][u][x, y] +
Tanh[y]*Derivative[0, 1][u][x, y] )
==========
Can someone do this ? It seems simple but infact, when i touch it, it
made the complex result. So what i want is how to obtain the
anaSolution.
Waiting for ur help...
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