8.87   ODE No. 1677

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

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

Mathematica: cpu = 46.986967 (sec), leaf count = 28 \[ \text {DSolve}\left [a y(x) y'(x)^2+b x+x^2 y''(x)=0,y(x),x\right ] \]

Maple: cpu = 2.309 (sec), leaf count = 101 \[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a}\,{ {\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+ {\it \_C1}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) = \left ( a{{\it \_a}}^{3}+b \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{3}+ \left ( 2\,{{\it \_a} }^{2}a+1 \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^ {2}+{\it \_a}\,{\it \_b} \left ( {\it \_a} \right ) a \right \} , \left \{ {\it \_a}={\frac {y \left ( x \right ) }{x}},{\it \_b} \left ( { \it \_a} \right ) =-{\frac {x}{-x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +y \left ( x \right ) }} \right \} , \left \{ x={{\rm e}^{\int \! {\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}},y \left ( x \right ) ={\it \_a}\,{{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right \} ] \right ) \right \} \]