3.909   ODE No. 909

\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {{x}^{3}+ \left ( y \left ( x \right ) \right ) ^{4}{x}^{3}+2\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}+x+{x}^{3} \left ( y \left ( x \right ) \right ) ^{6}+3\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{4}+3\,x \left ( y \left ( x \right ) \right ) ^{2}+1}{{x}^{5}y \left ( x \right ) }}=0} \]

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

Mathematica: cpu = 40.683666 (sec), leaf count = 64 \[ \text {DSolve}\left [y'(x)=\frac {x^3 y(x)^6+x^3 y(x)^4+x^3+3 x^2 y(x)^4+2 x^2 y(x)^2+3 x y(x)^2+x+1}{x^5 y(x)},y(x),x\right ] \]

Maple: cpu = 0.390 (sec), leaf count = 84 \[ \left \{ y \left ( x \right ) ={\frac {1}{x}\sqrt {x \left ( {\it RootOf} \left ( \int ^{{\it \_Z}}\! \left ( 2\,{{\it \_a}}^{3}+2\,{{\it \_a}}^{ 2}+1 \right ) ^{-1}{d{\it \_a}}x+x{\it \_C1}+1 \right ) x-1 \right ) }},y \left ( x \right ) =-{\frac {1}{x}\sqrt {x \left ( {\it RootOf} \left ( \int ^{{\it \_Z}}\! \left ( 2\,{{\it \_a}}^{3}+2\,{{\it \_a}}^{2}+1 \right ) ^{-1}{d{\it \_a}}x+x{\it \_C1}+1 \right ) x-1 \right ) }} \right \} \]