Re: Transform differential equation by tranformation rule

*To*: mathgroup at smc.vnet.net*Subject*: [mg111071] Re: Transform differential equation by tranformation rule*From*: janos <janostothmeister at gmail.com>*Date*: Mon, 19 Jul 2010 02:09:59 -0400 (EDT)*References*: <i1s6t2$a0a$1@smc.vnet.net>

On j=FAl. 17, 14:15, TrinhDao <hackerdarkr... at yahoo.com> wrote: > 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... This might help, try it. http://library.wolfram.com/infocenter/MathSource/4186/ J=E1nos