- #1
jimbo007
- 41
- 2
hi all
i have been trying to solve to following problem,
[tex]
\frac{\partial^2 u}{\partial x^2} - \frac{\partial^2 u}{\partial y^2}
+ 2\frac{\partial u}{\partial x} + u = 0
[/tex]
[tex]
u=u(x,y)
[/tex]
after a bit of work using the change of variables
[tex]
\zeta=\zeta(x,y)=y-x
[/tex]
and
[tex]
\eta=\eta(x,y)=y+x
[/tex]
i obtain
[tex]- 4\frac{\partial u}{\partial \zeta \partial \eta} = 2\frac{\partial u}{\partial\zeta} - 2\frac{\partial u}{\partial\eta}-u[/tex]
but i am unsure how to solve this, i used maple to solve this problem and it gave out a fairly harmless answer so i am pretty sure there would be any easy way to solve the above equation.
could someone kindly show me how to obtain a solution to this problem
i have been trying to solve to following problem,
[tex]
\frac{\partial^2 u}{\partial x^2} - \frac{\partial^2 u}{\partial y^2}
+ 2\frac{\partial u}{\partial x} + u = 0
[/tex]
[tex]
u=u(x,y)
[/tex]
after a bit of work using the change of variables
[tex]
\zeta=\zeta(x,y)=y-x
[/tex]
and
[tex]
\eta=\eta(x,y)=y+x
[/tex]
i obtain
[tex]- 4\frac{\partial u}{\partial \zeta \partial \eta} = 2\frac{\partial u}{\partial\zeta} - 2\frac{\partial u}{\partial\eta}-u[/tex]
but i am unsure how to solve this, i used maple to solve this problem and it gave out a fairly harmless answer so i am pretty sure there would be any easy way to solve the above equation.
could someone kindly show me how to obtain a solution to this problem
Last edited: