ODE
\[ 4 f(x) y(x) y''(x)=y'(x) \left (2 f'(x)-6 f(x) y(x)^2\right )+2 y(x)^3 f'(x)+3 f(x) g(x) y(x)^2+3 f(x) y'(x)^2-f(x) y(x)^4+4 f(x)^2 y(x) \] ODE Classification
(ODEtools/info) missing specification of intermediate function
Book solution method
TO DO
Mathematica ✗
cpu = 1.46515 (sec), leaf count = 0 , could not solve
DSolve[4*f[x]*y[x]*Derivative[2][y][x] == 4*f[x]^2*y[x] + 3*f[x]*g[x]*y[x]^2 - f[x]*y[x]^4 + 2*y[x]^3*Derivative[1][f][x] + (-6*f[x]*y[x]^2 + 2*Derivative[1][f][x])*Derivative[1][y][x] + 3*f[x]*Derivative[1][y][x]^2, y[x], x]
Maple ✗
cpu = 6.927 (sec), leaf count = 0 , could not solve
dsolve(4*f(x)*y(x)*diff(diff(y(x),x),x) = 3*f(x)*diff(y(x),x)^2+(2*diff(f(x),x)-6*f(x)*y(x)^2)*diff(y(x),x)+4*f(x)^2*y(x)+3*f(x)*g(x)*y(x)^2+2*diff(f(x),x)*y(x)^3-f(x)*y(x)^4, y(x),'implicit')
Mathematica raw input
DSolve[4*f[x]*y[x]*y''[x] == 4*f[x]^2*y[x] + 3*f[x]*g[x]*y[x]^2 - f[x]*y[x]^4 + 2*y[x]^3*f'[x] + (-6*f[x]*y[x]^2 + 2*f'[x])*y'[x] + 3*f[x]*y'[x]^2,y[x],x]
Mathematica raw output
DSolve[4*f[x]*y[x]*Derivative[2][y][x] == 4*f[x]^2*y[x] + 3*f[x]*g[x]*y[x]^2 - f[x]*y[x]^4 + 2*y[x]^3*Derivative[1][f][x] + (-6*f[x]*y[x]^2 + 2*Derivative[1][f][x])*Derivative[1][y][x] + 3*f[x]*Derivative[1][y][x]^2, y[x], x]
Maple raw input
dsolve(4*f(x)*y(x)*diff(diff(y(x),x),x) = 3*f(x)*diff(y(x),x)^2+(2*diff(f(x),x)-6*f(x)*y(x)^2)*diff(y(x),x)+4*f(x)^2*y(x)+3*f(x)*g(x)*y(x)^2+2*diff(f(x),x)*y(x)^3-f(x)*y(x)^4, y(x),'implicit')
Maple raw output
dsolve(4*f(x)*y(x)*diff(diff(y(x),x),x) = 3*f(x)*diff(y(x),x)^2+(2*diff(f(x),x)-6*f(x)*y(x)^2)*diff(y(x),x)+4*f(x)^2*y(x)+3*f(x)*g(x)*y(x)^2+2*diff(f(x),x)*y(x)^3-f(x)*y(x)^4, y(x),'implicit')