ODE
\[ y(x) y''(x)=y(x) f''(x)-f(x) y'(x)-f(x) y(x)^3+y'(x)^2+y(x)^4 \] ODE Classification
(ODEtools/info) missing specification of intermediate function
Book solution method
TO DO
Mathematica ✗
cpu = 0.496746 (sec), leaf count = 0 , could not solve
DSolve[y[x]*Derivative[2][y][x] == -(f[x]*y[x]^3) + y[x]^4 - f[x]*Derivative[1][y][x] + Derivative[1][y][x]^2 + y[x]*Derivative[2][f][x], y[x], x]
Maple ✗
cpu = 0.717 (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(diff(f(x),x),x)*y(x)-f(x)*y(x)^3+y(x)^4, y(x),'implicit')
Mathematica raw input
DSolve[y[x]*y''[x] == -(f[x]*y[x]^3) + y[x]^4 - f[x]*y'[x] + y'[x]^2 + y[x]*f''[x],y[x],x]
Mathematica raw output
DSolve[y[x]*Derivative[2][y][x] == -(f[x]*y[x]^3) + y[x]^4 - f[x]*Derivative[1][y][x] + Derivative[1][y][x]^2 + y[x]*Derivative[2][f][x], 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(diff(f(x),x),x)*y(x)-f(x)*y(x)^3+y(x)^4, 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(diff(f(x),x),x)*y(x)-f(x)*y(x)^3+y(x)^4, y(x),'implicit')