3.437   ODE No. 437

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

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

Mathematica: cpu = 0.274035 (sec), leaf count = 47 \[ \left \{\left \{y(x)\to \frac {x-2 \sqrt {a} c_1}{4 c_1^2}\right \},\left \{y(x)\to \frac {2 \sqrt {a} c_1+x}{4 c_1^2}\right \}\right \} \]

Maple: cpu = 0.515 (sec), leaf count = 36 \[ \left \{ y \left ( x \right ) =-{\frac {a}{4\,x}},y \left ( x \right ) ={ \it \_C1}\,x-\sqrt {{\it \_C1}\,a},y \left ( x \right ) ={\it \_C1}\,x+ \sqrt {{\it \_C1}\,a} \right \} \]