3.281   ODE No. 281

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

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

Mathematica: cpu = 0.062508 (sec), leaf count = 75 \[ \left \{\left \{y(x)\to \frac {1}{2} \left (e^{c_1}-\sqrt {4 e^{c_1} x+e^{2 c_1}-4 x^2}\right )\right \},\left \{y(x)\to \frac {1}{2} \left (\sqrt {4 e^{c_1} x+e^{2 c_1}-4 x^2}+e^{c_1}\right )\right \}\right \} \]

Maple: cpu = 0.047 (sec), leaf count = 53 \[ \left \{ y \left ( x \right ) ={\frac {1}{2\,{\it \_C1}} \left ( 1+\sqrt {-4\,{{\it \_C1}}^{2}{x}^{2}+4\,{\it \_C1}\,x+1} \right ) },y \left ( x \right ) =-{\frac {1}{2\,{\it \_C1}} \left ( -1+\sqrt {-4\,{{\it \_C1}} ^{2}{x}^{2}+4\,{\it \_C1}\,x+1} \right ) } \right \} \]