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Student Support Forum: 'Solving a differential equation' topicStudent Support Forum > General > Archives > "Solving a differential equation"

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foobar
07/05/12 06:41am

Hi, I'm currently trying to solve a specific differential equation:

d^2 X(x,z)/dx^2 = 2ik dX(x,z)/dz

This is what I typed into Mathematica:
DSolve[ D[X[x, z], {x, 2}] == 2*I*k*D[X[x, z], z], X[x, z], {x, z}]

And all it gives me is exact this, only the derivatives are written a bit more nicely:
DSolve[(X^(2,0))[x,z]==2 I k (X^(0,1))[x,z],X[x,z],{x,z}]

Where's the mistake here? The equation is solvable, it's for a Gaußian beam from laser optics (see Wikipedia, for example).

What do I have to do, in order to make Mathematica give me the result?

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