Solving a system of differential equations

Questions
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1

I’ve just started learning Mathematica. I have entered code to solve a system of differential equations, of which I know the solution. When I evaluate the notebook, I am just given my code rewritten, with no error message. I’m not sure what is wrong with my code. Any advice would be greatly appreciated.

Dsolve[{Derivative[1][A][t] + ik A[t] - (m + 1)^(.5) B[t] == 0, 
  B'[t] + (m + 1)^(.5) A[t] + m^(.5) F[t] == 0, 
  F'[t] - ik F[t] - m^(.5) B[t] == 0, 
  A[0] == 0, B[0] == 0, F[0] == 0}, 
  {A[t], B[t], C[t]}, t]
2

Hi,

there are some issues with it. First the command is DSolve not Dsolve. Capitalisation is important in Mathematica. Second, you have Three functions that you declare as A,B and C. One of the differential equations contains an F’ and F, but none contains a C. So I changed the function to:

DSolve[{A'[t] + ik A[t] - (m + 1)^(.5) B[t] == 0, B'[t] + (m + 1)^(.5) A[t] + m^(.5) F[t] == 0, F'[t] - ik F[t] - m^(.5) B[t] == 0, A[0] == 0, B[0] == 0, F[0] == 0}, {A[t], B[t], F[t]}, t]

It finds

(*{{A[t] -> 0, B[t] -> 0, F[t] -> 0}}*)

which appears to be the solution.

Best wishes,

M.

3

Great, thanks! That works for me too. I was staring at that for hours, I really appreciate the help!