2.1885   ODE No. 1885

\[ \left \{t x'(t)-t y'(t)-2 y(t)=0,t x''(t)+2 x'(t)+t x(t)=0\right \} \]

✓ Mathematica : cpu = 0.021659 (sec), leaf count = 66

DSolve[{-2*y[t] + t*Derivative[1][x][t] - t*Derivative[1][y][t] == 0, t*x[t] + 2*Derivative[1][x][t] + t*Derivative[2][x][t] == 0},{x[t], y[t]},t]
 

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

✓ Maple : cpu = 0.112 (sec), leaf count = 47

dsolve({t*diff(diff(x(t),t),t)+2*diff(x(t),t)+t*x(t) = 0, t*diff(x(t),t)-t*diff(y(t),t)-2*y(t) = 0})
 

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