2.1925   ODE No. 1925

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

✓ Mathematica : cpu = 0.0205026 (sec), leaf count = 31

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

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

✓ Maple : cpu = 0.314 (sec), leaf count = 144

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

\[\left [\left \{x \left (t \right ) = -\frac {t^{2}}{3}\right \}, \left \{y \left (t \right ) = -\frac {t^{3}}{27 a}\right \}\right ]\]