3.425   ODE No. 425

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

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

Mathematica: cpu = 0.270034 (sec), leaf count = 59 \[ \left \{\left \{y(x)\to -\frac {e^{c_1} \left (e^{c_1}-2 x\right )}{2 \left (e^{c_1}+2\right )}\right \},\left \{y(x)\to -\frac {2 e^{c_1} \left (2 e^{c_1}-x\right )}{2 e^{c_1}+1}\right \}\right \} \]

Maple: cpu = 0.562 (sec), leaf count = 59 \[ \left \{ y \left ( x \right ) ={\frac { \left ( -{{\it \_C1}}^{2}+{\it \_C1} \right ) x}{-{\it \_C1}+1}}-{\frac {{{\it \_C1}}^{2}}{-{\it \_C1} +1}},y \left ( x \right ) =x+2-2\,\sqrt {1+x},y \left ( x \right ) =x+2+2 \,\sqrt {1+x} \right \} \]