2.1913   ODE No. 1913

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

✓ Mathematica : cpu = 0.0404335 (sec), leaf count = 64

DSolve[{Derivative[1][x][t] == -(x[t]*(x[t] + y[t])), Derivative[1][y][t] == y[t]*(x[t] + y[t])},{x[t], y[t]},t]
 

\[\left \{\left \{y(t)\to -\sqrt {c_1} \cot \left (\sqrt {c_1} t-\sqrt {c_1} c_2\right ),x(t)\to -\sqrt {c_1} \tan \left (\sqrt {c_1} t-\sqrt {c_1} c_2\right )\right \}\right \}\]

✓ Maple : cpu = 0.117 (sec), leaf count = 57

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

\[\left [\{x \left (t \right ) = 0\}, \left \{y \left (t \right ) = \frac {1}{-t +c_{1}}\right \}\right ]\]