2.1910   ODE No. 1910

\[ \left \{t x'(t)=2 x(t)-t,t^3 y'(t)=t^2 y(t)-x(t)+t,t^4 z'(t)=t^3 z(t)-t^2 y(t)-x(t)+t\right \} \]

✓ Mathematica : cpu = 0.0091341 (sec), leaf count = 39

DSolve[{t*Derivative[1][x][t] == -t + 2*x[t], t^3*Derivative[1][y][t] == t - x[t] + t^2*y[t], t^4*Derivative[1][z][t] == t - x[t] - t^2*y[t] + t^3*z[t]},{x[t], y[t], z[t]},t]
 

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

✓ Maple : cpu = 0.079 (sec), leaf count = 37

dsolve({t*diff(x(t),t) = 2*x(t)-t, t^3*diff(y(t),t) = -x(t)+t^2*y(t)+t, t^4*diff(z(t),t) = -x(t)-t^2*y(t)+t^3*z(t)+t})
 

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