ODE
\[ y''(x)+3 y(x) y'(x)=f(x)+g(x) y(x)-y(x)^3 \] ODE Classification
[NONE]
Book solution method
TO DO
Mathematica ✗
cpu = 4.8446 (sec), leaf count = 0 , could not solve
DSolve[3*y[x]*Derivative[1][y][x] + Derivative[2][y][x] == f[x] + g[x]*y[x] - y[x]^3, y[x], x]
Maple ✗
cpu = 0.009 (sec), leaf count = 0 , result contains DESol
\[ \left \{ y \left ( x \right ) ={\frac {{\frac {\rm d}{{\rm d}x}}{\it DESol} \left ( \left \{ -f \left ( x \right ) {\it \_Y} \left ( x \right ) -g \left ( x \right ) {\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) +{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}{\it \_Y} \left ( x \right ) \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) }{{\it DESol} \left ( \left \{ -f \left ( x \right ) {\it \_Y} \left ( x \right ) -g \left ( x \right ) {\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) +{\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}{\it \_Y} \left ( x \right ) \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) }} \right \} \]
Mathematica raw input
DSolve[3*y[x]*y'[x] + y''[x] == f[x] + g[x]*y[x] - y[x]^3,y[x],x]
Mathematica raw output
DSolve[3*y[x]*Derivative[1][y][x] + Derivative[2][y][x] == f[x] + g[x]*y[x] - y[x]^3, y[x], x]
Maple raw input
dsolve(diff(diff(y(x),x),x)+3*y(x)*diff(y(x),x) = f(x)+g(x)*y(x)-y(x)^3, y(x),'implicit')
Maple raw output
y(x) = diff(DESol({-f(x)*_Y(x)-g(x)*diff(_Y(x),x)+diff(diff(diff(_Y(x),x),x),x)},{_Y(x)}),x)/DESol({-f(x)*_Y(x)-g(x)*diff(_Y(x),x)+diff(diff(diff(_Y(x),x),x),x)},{_Y(x)})