##### 4.45.33 $$y''''(x)+3 y(x) \left (f''(x)+3 f(x)^2\right )+10 f'(x) y'(x)+10 f(x) y''(x)=0$$

ODE
$y''''(x)+3 y(x) \left (f''(x)+3 f(x)^2\right )+10 f'(x) y'(x)+10 f(x) y''(x)=0$ ODE Classiﬁcation

odeadvisor timed out

Book solution method
TO DO

Mathematica
cpu = 0.299294 (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 = 0.491 (sec), leaf count = 0 , result contains DESol or ODESolStruc

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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 + Derivativ
e[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))

Maple raw output

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