# Mathematica DSolve does nothing

So I am trying to solve:

***DSolve[{Derivative[1][c1][
t] == (0. -
9.48262*10^33 I) ((-2.40987*10^-22 + 4.97993*10^-23 B^2 +
1.84752*10^-23 \[Xi]1 + 1.24163*10^-23 \[Xi]2) c1[
t] + (-3.68681*10^-23 + 3.1645*10^-24 B^2 +
2.0369*10^-24 \[Xi]1 + 2.0369*10^-24 \[Xi]2) c2[t]),
Derivative[1][c2][
t] == (0. -
9.48262*10^33 I) ((-3.68681*10^-23 + 3.1645*10^-24 B^2 +
2.0369*10^-24 \[Xi]1 + 2.0369*10^-24 \[Xi]2) c1[
t] + (-2.40987*10^-22 + 4.97993*10^-23 B^2 +
1.24163*10^-23 \[Xi]1 + 1.84752*10^-23 \[Xi]2) c2[t]),
c1[0] == 0.948683, c2[0] == 0.316228}, {c1[t], c2[t]}, t]***


But mathematica does nothing; it just gives me back the expression. What am I doing wrong? Thanks!

Clear["Global*"]


Rationalize the equations

eqns = {Derivative[1][c1][
t] == (0. -
9.48262*10^33 I) ((-2.40987*10^-22 + 4.97993*10^-23 B^2 +
1.84752*10^-23 \[Xi]1 + 1.24163*10^-23 \[Xi]2) c1[
t] + (-3.68681*10^-23 + 3.1645*10^-24 B^2 + 2.0369*10^-24 \[Xi]1 +
2.0369*10^-24 \[Xi]2) c2[t]),
Derivative[1][c2][
t] == (0. -
9.48262*10^33 I) ((-3.68681*10^-23 + 3.1645*10^-24 B^2 +
2.0369*10^-24 \[Xi]1 + 2.0369*10^-24 \[Xi]2) c1[
t] + (-2.40987*10^-22 + 4.97993*10^-23 B^2 +
1.24163*10^-23 \[Xi]1 + 1.84752*10^-23 \[Xi]2) c2[t]),
c1[0] == 0.948683, c2[0] == 0.316228} // Rationalize[#, 0] &;

sol = DSolve[eqns, {c1, c2}, t];


Verifying the solutions,

eqns /. sol // Simplify

(* {{True, True, True, True}} *)

• It worked, thanks a lot! But could you explain why? Nov 20, 2020 at 13:33
• Exact solvers (e.g., Solve, Reduce, DSolve) can encounter difficulties in working with approximate real numbers. For example, you may encounter a warning message that Solve was unable to solve an equation with inexact coefficients, that it solved by rationalizing the coefficients, and then numericized the result. However, Mma does not appear to try this workaround with DSolve. Consequently, when DSolve` returns unevaluated with approximate real numbers, it is worth trying to solve after converting all equations to exact forms. This won't help in all cases, but did in this case. Nov 20, 2020 at 14:01