ODE
\[ y(x) y''(x)=-y(x) f'(x)+f(x) y'(x)+y'(x)^2+y(x)^3 \] ODE Classification
(ODEtools/info) missing specification of intermediate function
Book solution method
TO DO
Mathematica ✗
cpu = 0.229892 (sec), leaf count = 0 , could not solve
DSolve[y[x]*Derivative[2][y][x] == y[x]^3 - y[x]*Derivative[1][f][x] + f[x]*Derivative[1][y][x] + Derivative[1][y][x]^2, y[x], x]
Maple ✗
cpu = 0.477 (sec), leaf count = 0 , could not solve
dsolve(y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2+f(x)*diff(y(x),x)-diff(f(x),x)*y(x)+y(x)^3, y(x),'implicit')
Mathematica raw input
DSolve[y[x]*y''[x] == y[x]^3 - y[x]*f'[x] + f[x]*y'[x] + y'[x]^2,y[x],x]
Mathematica raw output
DSolve[y[x]*Derivative[2][y][x] == y[x]^3 - y[x]*Derivative[1][f][x] + f[x]*Derivative[1][y][x] + Derivative[1][y][x]^2, y[x], x]
Maple raw input
dsolve(y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2+f(x)*diff(y(x),x)-diff(f(x),x)*y(x)+y(x)^3, y(x),'implicit')
Maple raw output
dsolve(y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2+f(x)*diff(y(x),x)-diff(f(x),x)*y(x)+y(x)^3, y(x),'implicit')