8.172   ODE No. 1762

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

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

Mathematica: cpu = 52.685690 (sec), leaf count = 39 \[ \text {DSolve}\left [a y(x) y'(x)+b x y(x)^3+x y(x) y''(x)-x y'(x)^2=0,y(x),x\right ] \]

Maple: cpu = 2.215 (sec), leaf count = 106 \[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\frac {{\it \_a }}{ \left ( {{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right ) ^{2}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) ={\it \_a }\, \left ( b{\it \_a}-2\,a+2 \right ) \left ( {\it \_b} \left ( {\it \_a } \right ) \right ) ^{3}+ \left ( a-1 \right ) \left ( {\it \_b} \left ( { \it \_a} \right ) \right ) ^{2}-{\frac {{\it \_b} \left ( {\it \_a} \right ) }{{\it \_a}}} \right \} , \left \{ {\it \_a}={x}^{2}y \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) ={\frac {1}{{x}^{2} \left ( x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +2\,y \left ( x \right ) \right ) }} \right \} , \left \{ x={{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}},y \left ( x \right ) ={\frac {{\it \_a}}{ \left ( {{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right ) ^{2} }} \right \} ] \right ) \right \} \]