4.45.33 $y^{⁗}(x)+3y(x)(f^{″}(x)+3f(x{)}^2)+10f^{\prime }(x)y^{\prime }(x)+10f(x)y^{″}(x)=0$

ODE
$$y^{⁗}(x)+3y(x)(f^{″}(x)+3f(x{)}^2)+10f^{\prime }(x)y^{\prime }(x)+10f(x)y^{″}(x)=0$$ 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

$$\{y\left(x\right)={\left(\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}(\{\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}\mathit{\_}\mathit{Y}\left(x\right)+f\left(x\right)\mathit{\_}\mathit{Y}\left(x\right)\},\left\{\mathit{\_}\mathit{Y}\left(x\right)\right\})\right)}^3\}$$

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),'implicit')

Maple raw output

y(x) = DESol({diff(diff(_Y(x),x),x)+f(x)*_Y(x)},{_Y(x)})^3