Coupled first order differential equations

  • #1
I am trying to solve a problem (not homework, too old for that! lol!) which involves the time dependent schrodinger equation for magnetic moment in time-dependent magnetic fields. I end up with the following that needs to be solved:

x' = -i*(b*t-a*t^2)*x - i*c*y
y' = -i*c*x - i*(a*t^2-b*t)*y;

where i^2 = -1.

These look like 2 coupled 1st order ODE, but are in fact 4 coupled 1st order due to the imaginary parts. Any hints?
 

Answers and Replies

  • #2
479
32
The easiest way is a nonlinear solver, like Mathematica, Maple or MATLAB. I guess you could even use Excel with the Solver nonlinear package.

I'm not a mathematician, but why can't you solve one ODE and substitute into the other one?
 

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