2.1762   ODE No. 1762

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

\[ a y(x) y'(x)+b x y(x)^3-x y'(x)^2+x y(x) y''(x)=0 \] Mathematica : cpu = 48.1884 (sec), leaf count = 0 , could not solve

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

Maple : cpu = 1.019 (sec), leaf count = 108

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