ODE
\[ y'''(x)+y'(x) \left (2 f'(x)^2+f'(x)+4 g(x)\right )+2 y(x) \left (2 f(x) g(x)+g'(x)\right )+3 f(x) y''(x)=0 \] ODE Classification
(ODEtools/info) missing specification of intermediate function
Book solution method
TO DO
Mathematica ✗
cpu = 0.0230963 (sec), leaf count = 0 , could not solve
DSolve[2*y[x]*(2*f[x]*g[x] + Derivative[1][g][x]) + (4*g[x] + Derivative[1][f][x] + 2*Derivative[1][f][x]^2)*Derivative[1][y][x] + 3*f[x]*Derivative[2][y][x] + Derivative[3][y][x] == 0, y[x], x]
Maple ✗
cpu = 0.093 (sec), leaf count = 0 , result contains DESol
\[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}{\it \_Y} \left ( x \right ) +3\,f \left ( x \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}{\it \_Y} \left ( x \right ) + \left ( {\frac {\rm d}{{\rm d}x}}f \left ( x \right ) +2\, \left ( {\frac {\rm d}{{\rm d}x}}f \left ( x \right ) \right ) ^{2}+4\,g \left ( x \right ) \right ) {\frac {\rm d}{{\rm d}x}}{\it \_Y} \left ( x \right ) + \left ( 4\,f \left ( x \right ) g \left ( x \right ) +2\,{\frac {\rm d}{{\rm d}x}}g \left ( x \right ) \right ) {\it \_Y} \left ( x \right ) \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]
Mathematica raw input
DSolve[2*y[x]*(2*f[x]*g[x] + g'[x]) + (4*g[x] + f'[x] + 2*f'[x]^2)*y'[x] + 3*f[x]*y''[x] + y'''[x] == 0,y[x],x]
Mathematica raw output
DSolve[2*y[x]*(2*f[x]*g[x] + Derivative[1][g][x]) + (4*g[x] + Derivative[1][f][x] + 2*Derivative[1][f][x]^2)*Derivative[1][y][x] + 3*f[x]*Derivative[2][y][x] + Derivative[3][y][x] == 0, y[x], x]
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)+3*f(x)*diff(diff(y(x),x),x)+(diff(f(x),x)+2*diff(f(x),x)^2+4*g(x))*diff(y(x),x)+2*(2*f(x)*g(x)+diff(g(x),x))*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = DESol({diff(diff(diff(_Y(x),x),x),x)+3*f(x)*diff(diff(_Y(x),x),x)+(diff(f(x),x)+2*diff(f(x),x)^2+4*g(x))*diff(_Y(x),x)+(4*f(x)*g(x)+2*diff(g(x),x))*_Y(x)},{_Y(x)})