3.444   ODE No. 444

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

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

Mathematica: cpu = 0.143518 (sec), leaf count = 103 \[ \left \{\left \{y(x)\to -\frac {4 e^{-2 c_1}}{e^{2 c_1} x-2}\right \},\left \{y(x)\to -\frac {4 e^{-2 c_1}}{e^{2 c_1} x+2}\right \},\left \{y(x)\to -\frac {e^{-2 c_1}}{2 \left (2 e^{2 c_1} x-1\right )}\right \},\left \{y(x)\to -\frac {e^{-2 c_1}}{2 \left (2 e^{2 c_1} x+1\right )}\right \}\right \} \]

Maple: cpu = 1.045 (sec), leaf count = 121 \[ \left \{ y \left ( x \right ) =4\,x,y \left ( x \right ) =-{\frac {{{\it \_C1}}^{2} \left ( \sqrt {2}{\it \_C1}-2\,x \right ) }{2\,{{\it \_C1}}^{ 2}-4\,{x}^{2}}},y \left ( x \right ) =-2\,{\frac {{{\it \_C1}}^{2} \left ( \sqrt {2}{\it \_C1}-x \right ) }{2\,{{\it \_C1}}^{2}-{x}^{2}}}, y \left ( x \right ) =2\,{\frac {{{\it \_C1}}^{2} \left ( \sqrt {2}{\it \_C1}+x \right ) }{2\,{{\it \_C1}}^{2}-{x}^{2}}},y \left ( x \right ) ={ \frac {{{\it \_C1}}^{2} \left ( \sqrt {2}{\it \_C1}+2\,x \right ) }{2\,{ {\it \_C1}}^{2}-4\,{x}^{2}}} \right \} \]