# Solving a system of ODEs with DSolve

I am trying to solve a system of ODEs using DSolve

system = {y'[t] == (1 + (x[t]/0.6)^2)^-1 - y[t], x'[t] == (1 + (y[t]/0.6)^2)^-1 - x[t]};

sol = DSolve[system, {y, x}, t];


Sadly Mathematica returns the input as an output.

Any suggestions ?

• Use NDSolve or ParametricNDSolveValue? Nonlinear equations are hard, as in rarely solvable symbolically. Do you know if this system has a solution in terms of standard functions? The subset of solutions (and there is one by symmetry) where y == x can be found thus: DSolve[Derivative[1][y][t] == 1/(1 + (25 y[t]^2)/9) - y[t], y, t]... – Michael E2 Jan 5 '15 at 0:19
• Thanks @Michael, for me Parametric function might be off the table - dont know all the details, but I did try NDSolve beforehand, truth be told with random IVPs as 1 for both y[0] and x[0], and t ranging from 0 to 20, thus like this: system = {y'[t] == (1 + ((x[t]/0.6)^2)^-1) - y[t], x'[t] == (1 + ((y[t]/0.6)^2)^-1) - x[t]}; initialValues = {y[0] == 1, x[0] == 1}; sol = NDSolve[Join[system, initialValues], {y, x}, {t, 0, 20}]; But this only gave me another error: No derivatives of dependent variables were found in the equations <- no solution exists? Btw it's Thornley method for plants – guesXy Jan 5 '15 at 0:52
• There must be some definition that is causing the error in NDSolve. Your code returned a solution without error for me. You could try Clear[x,y] and then run it again. – Jerro39 Jan 5 '15 at 4:33
• @Jerro39 strange, i tried with clear and still ge thte same: No derivatives of dependent variables were found in the equations <- can you maybe copy/paste the exact code you entered? Also i'm on version 10 of Mathematica, same for you? – guesXy Jan 5 '15 at 8:36
• I copied and pasted the code in your comment above into a fresh Mathematica kernel. I'm using version 9.0 for Linux x86 (64 bit). Maybe try to copy, paste and evaluate the code in the comment above in a new MMA kernel? – Jerro39 Jan 5 '15 at 15:28