4.36.41 \(y''(x)+y(x) y'(x)=12 f'(x)-12 f(x) y(x)+y(x)^3\)

ODE
\[ y''(x)+y(x) y'(x)=12 f'(x)-12 f(x) y(x)+y(x)^3 \] ODE Classification

(ODEtools/info) missing specification of intermediate function

Book solution method
TO DO

Mathematica
cpu = 2.39128 (sec), leaf count = 0 , could not solve

DSolve[y[x]*Derivative[1][y][x] + Derivative[2][y][x] == -12*f[x]*y[x] + y[x]^3 + 12*Derivative[1][f][x], y[x], x]

Maple
cpu = 0.497 (sec), leaf count = 0 , could not solve

dsolve(diff(diff(y(x),x),x)+y(x)*diff(y(x),x) = 12*diff(f(x),x)-12*f(x)*y(x)+y(x)^3, y(x),'implicit')

Mathematica raw input

DSolve[y[x]*y'[x] + y''[x] == -12*f[x]*y[x] + y[x]^3 + 12*f'[x],y[x],x]

Mathematica raw output

DSolve[y[x]*Derivative[1][y][x] + Derivative[2][y][x] == -12*f[x]*y[x] + y[x]^3 
+ 12*Derivative[1][f][x], y[x], x]

Maple raw input

dsolve(diff(diff(y(x),x),x)+y(x)*diff(y(x),x) = 12*diff(f(x),x)-12*f(x)*y(x)+y(x)^3, y(x),'implicit')

Maple raw output

dsolve(diff(diff(y(x),x),x)+y(x)*diff(y(x),x) = 12*diff(f(x),x)-12*f(x)*y(x)+y(x
)^3, y(x),'implicit')