2.1900   ODE No. 1900

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ \left \{x'(t)=4 x(t),y'(t)=x(t)-2 y(t),z'(t)=x(t)-4 y(t)+z(t)\right \} \] Mathematica : cpu = 0.0088893 (sec), leaf count = 94

\[\left \{\left \{x(t)\to c_1 e^{4 t},y(t)\to \frac {1}{6} c_1 e^{-2 t} \left (e^{6 t}-1\right )+c_2 e^{-2 t},z(t)\to \frac {1}{9} c_1 e^{-2 t} \left (e^{3 t}+e^{6 t}-2\right )-\frac {4}{3} c_2 e^{-2 t} \left (e^{3 t}-1\right )+c_3 e^t\right \}\right \}\] Maple : cpu = 0.116 (sec), leaf count = 50

\[\left \{\left \{x \left (t \right ) = c_{3} {\mathrm e}^{4 t}, y \left (t \right ) = c_{2} {\mathrm e}^{-2 t}+\frac {c_{3} {\mathrm e}^{4 t}}{6}, z \left (t \right ) = c_{1} {\mathrm e}^{t}+\frac {4 c_{2} {\mathrm e}^{-2 t}}{3}+\frac {c_{3} {\mathrm e}^{4 t}}{9}\right \}\right \}\]