2.1682   ODE No. 1682

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

\[ x^3 \left (y(x) y'(x)+y''(x)-y(x)^3\right )+12 x y(x)+24=0 \] Mathematica : cpu = 21.8291 (sec), leaf count = 0 , could not solve

DSolve[24 + 12*x*y[x] + x^3*(-y[x]^3 + y[x]*Derivative[1][y][x] + Derivative[2][y][x]) == 0, y[x], x]

Maple : cpu = 1.024 (sec), leaf count = 94

\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a}\,{{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) =- \left ( \left ( {{\it \_a}}^{3}+{{\it \_a}}^{2}-14\,{\it \_a}-24 \right ) {\it \_b} \left ( {\it \_a} \right ) +{\it \_a}-3 \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2} \right \} , \left \{ {\it \_a}=xy \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) =-{\frac {1}{x \left ( x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +y \left ( x \right ) \right ) }} \right \} , \left \{ x= \left ( {{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right ) ^{-1},y \left ( x \right ) ={\it \_a}\,{{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right \} ] \right ) \right \} \]