ODE
\[ y''''(x)+3 y(x) \left (f''(x)+3 f(x)^2\right )+10 f'(x) y'(x)+10 f(x) y''(x)=0 \] ODE Classification
(ODEtools/info) missing specification of intermediate function
Book solution method
TO DO
Mathematica ✗
cpu = 0.0186606 (sec), leaf count = 0 , could not solve
DSolve[10*Derivative[1][f][x]*Derivative[1][y][x] + 3*y[x]*(3*f[x]^2 + Derivative[2][f][x]) + 10*f[x]*Derivative[2][y][x] + Derivative[4][y][x] == 0, y[x], x]
Maple ✗
cpu = 0.113 (sec), leaf count = 0 , result contains DESol
\[ \left \{ y \left ( x \right ) = \left ( {\it DESol} \left ( \left \{ {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}{\it \_Y} \left ( x \right ) +f \left ( x \right ) {\it \_Y} \left ( x \right ) \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right ) ^{3} \right \} \]
Mathematica raw input
DSolve[10*f'[x]*y'[x] + 3*y[x]*(3*f[x]^2 + f''[x]) + 10*f[x]*y''[x] + y''''[x] == 0,y[x],x]
Mathematica raw output
DSolve[10*Derivative[1][f][x]*Derivative[1][y][x] + 3*y[x]*(3*f[x]^2 + Derivative[2][f][x]) + 10*f[x]*Derivative[2][y][x] + Derivative[4][y][x] == 0, y[x], x]
Maple raw input
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)+10*f(x)*diff(diff(y(x),x),x)+10*diff(f(x),x)*diff(y(x),x)+3*(diff(diff(f(x),x),x)+3*f(x)^2)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = DESol({diff(diff(_Y(x),x),x)+f(x)*_Y(x)},{_Y(x)})^3