2.1901   ODE No. 1901

\[ \left \{x'(t)=y(t)-z(t),y'(t)=x(t)+y(t),z'(t)=x(t)+z(t)\right \} \]

✓ Mathematica : cpu = 0.0103042 (sec), leaf count = 105

DSolve[{Derivative[1][x][t] == y[t] - z[t], Derivative[1][y][t] == x[t] + y[t], Derivative[1][z][t] == x[t] + z[t]},{x[t], y[t], z[t]},t]
 

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

✓ Maple : cpu = 0.064 (sec), leaf count = 43

dsolve({diff(x(t),t) = y(t)-z(t), diff(y(t),t) = x(t)+y(t), diff(z(t),t) = x(t)+z(t)})
 

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