2.1624   ODE No. 1624

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

\[ y(x) \left (a f(x)^2+3 f'(x)+\frac {3 f'(x)^2}{f(x)^2}-\frac {f''(x)}{f(x)}\right )+b f(x)^3-\left (\frac {f'(x)}{f(x)}+f(x)\right ) \left (3 y'(x)+y(x)^2\right )+y(x) y'(x)+y''(x)-y(x)^3=0 \] Mathematica : cpu = 0.62962 (sec), leaf count = 0 , could not solve

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

Maple : cpu = 1.872 (sec), leaf count = 131

\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( f \left ( {\it RootOf} \left ( \int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}-\int ^{{\it \_Z}}\!f \left ( {\it \_f} \right ) {d{\it \_f}} \right ) \right ) {\it \_a},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) = \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2} \left ( \left ( -{{\it \_a}}^{3}-{{\it \_a}}^{2}+{\it \_a}\,a+b \right ) {\it \_b} \left ( {\it \_a} \right ) +{\it \_a}-3 \right ) \right \} , \left \{ {\it \_a}={\frac {y \left ( x \right ) }{f \left ( x \right ) }},{\it \_b} \left ( {\it \_a} \right ) ={\frac { \left ( f \left ( x \right ) \right ) ^{3}}{f \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( {\frac {\rm d}{{\rm d}x}}f \left ( x \right ) \right ) y \left ( x \right ) }} \right \} , \left \{ x={\it RootOf} \left ( \int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}-\int ^{{\it \_Z}}\!f \left ( {\it \_f} \right ) {d{\it \_f}} \right ) ,y \left ( x \right ) =f \left ( {\it RootOf} \left ( \int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}-\int ^{{\it \_Z}}\!f \left ( {\it \_f} \right ) {d{\it \_f}} \right ) \right ) {\it \_a} \right \} ] \right ) \right \} \]