2.1684   ODE No. 1684

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

\[ x y(x) \left (a-2 x^2 y(x)^2+3 x y(x)\right )+b+x^2 (2 x y(x)+9) y'(x)+2 x^3 y''(x)=0 \] Mathematica : cpu = 46.8498 (sec), leaf count = 0 , could not solve

DSolve[b + x*y[x]*(a + 3*x*y[x] - 2*x^2*y[x]^2) + x^2*(9 + 2*x*y[x])*Derivative[1][y][x] + 2*x^3*Derivative[2][y][x] == 0, y[x], x]

Maple : cpu = 1.4 (sec), leaf count = 100

\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a}\,{{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) ={\frac { \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2} \left ( \left ( -2\,{{\it \_a}}^{3}+{{\it \_a}}^{2}+ \left ( a-5 \right ) {\it \_a}+b \right ) {\it \_b} \left ( {\it \_a} \right ) -2\,{\it \_a}-3 \right ) }{2}} \right \} , \left \{ {\it \_a}=xy \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) =-{\frac {1}{x \left ( x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +y \left ( x \right ) \right ) }} \right \} , \left \{ x= \left ( {{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right ) ^{-1},y \left ( x \right ) ={\it \_a}\,{{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right \} ] \right ) \right \} \]