8.45   ODE No. 1635

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

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

Mathematica: cpu = 101.517891 (sec), leaf count = 23 \[ \text {DSolve}\left [a y'(x)^2+b y(x)+y''(x)=0,y(x),x\right ] \]

Maple: cpu = 0.109 (sec), leaf count = 79 \[ \left \{ \int ^{y \left ( x \right ) }\!-2\,{\frac {a}{\sqrt {4\,{ {\rm e}^{-2\,a{\it \_a}}}{\it \_C1}\,{a}^{2}-4\,{\it \_a}\,ab+2\,b}}}{ d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!2\,{\frac {a}{ \sqrt {4\,{{\rm e}^{-2\,a{\it \_a}}}{\it \_C1}\,{a}^{2}-4\,{\it \_a}\, ab+2\,b}}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]