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 = 0.0102984 (sec), leaf count = 88

\[\left \{\left \{x(t)\to c_1 e^{4 t},y(t)\to \frac {1}{6} e^{-2 t} \left (c_1 \left (e^{6 t}-1\right )+6 c_2\right ),z(t)\to \frac {1}{9} e^{-2 t} \left (c_1 \left (e^{3 t}+e^{6 t}-2\right )-12 c_2 \left (e^{3 t}-1\right )+9 c_3 e^{3 t}\right )\right \}\right \}\]

Maple : cpu = 0.084 (sec), leaf count = 50

\[ \left \{ \left \{ x \left ( t \right ) ={\it \_C3}\,{{\rm e}^{4\,t}},y \left ( t \right ) ={\frac {{\it \_C3}\,{{\rm e}^{4\,t}}}{6}}+{{\rm e}^{-2\,t}}{\it \_C2},z \left ( t \right ) ={\frac {{\it \_C3}\,{{\rm e}^{4\,t}}}{9}}+{\it \_C1}\,{{\rm e}^{t}}+{\frac {4\,{{\rm e}^{-2\,t}}{\it \_C2}}{3}} \right \} \right \} \]