3.19   ODE No. 19

\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( y \left ( x \right ) +x \right ) ^{2}=0} \]

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

Mathematica: cpu = 0.009001 (sec), leaf count = 30 \[ \left \{\left \{y(x)\to \frac {1}{c_1 e^{2 i x}-\frac {i}{2}}-x-i\right \}\right \} \]

Maple: cpu = 0.047 (sec), leaf count = 16 \[ \left \{ y \left ( x \right ) =-x-\tan \left ( -x+{\it \_C1} \right ) \right \} \]

Sage: cpu = 0.052 (sec), leaf count = 0 \[ \left [\left [\left [x = c - \arctan \left (\sqrt {t}\right ), y\left (x\right ) = -x - \sqrt {t}\right ], \left [x = c + \arctan \left (\sqrt {t}\right ), y\left (x\right ) = -x + \sqrt {t}\right ]\right ], \text {\texttt {lagrange}}\right ] \]