3.442   ODE No. 442

\[ \boxed { {x}^{2} \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+ \left ( {x}^{2}y \left ( x \right ) -2\,xy \left ( x \right ) +{x}^{3} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( \left ( y \left ( x \right ) \right ) ^{2}-{x}^{2}y \left ( x \right ) \right ) \left ( 1-x \right ) =0} \]

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

Mathematica: cpu = 0.007501 (sec), leaf count = 28 \[ \left \{\left \{y(x)\to c_1 e^{-x} x\right \},\left \{y(x)\to c_1 x-x^2\right \}\right \} \]

Maple: cpu = 0.0 (sec), leaf count = 21 \[ \left \{ y \left ( x \right ) = \left ( -x+{\it \_C1} \right ) x,y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-x}}x \right \} \]