8.47   ODE No. 1637

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

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

Mathematica: cpu = 30.477870 (sec), leaf count = 29 \[ \text {DSolve}\left [a y'(x)^2+b y'(x)+c y(x)+y''(x)=0,y(x),x\right ] \]

Maple: cpu = 0.359 (sec), leaf count = 58 \[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a},[ \left \{ \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( { \it \_a} \right ) \right ) {\it \_b} \left ( {\it \_a} \right ) +a \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}+{\it \_b} \left ( {\it \_a} \right ) b+c{\it \_a}=0 \right \} , \left \{ {\it \_a}= y \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) ={\frac {\rm d} {{\rm d}x}}y \left ( x \right ) \right \} , \left \{ x=\int \! \left ( { \it \_b} \left ( {\it \_a} \right ) \right ) ^{-1}\,{\rm d}{\it \_a}+{ \it \_C1},y \left ( x \right ) ={\it \_a} \right \} ] \right ) \right \} \]