ODE
\[ 2 y(x) y''(x)=-2 y(x)^2 \left (f'(x)+f(x)^2\right )-3 f(x) y(x) y'(x)+y'(x)^2+8 y(x)^3 \] ODE Classification
(ODEtools/info) missing specification of intermediate function
Book solution method
TO DO
Mathematica ✗
cpu = 0.513298 (sec), leaf count = 0 , could not solve
DSolve[2*y[x]*Derivative[2][y][x] == 8*y[x]^3 - 2*y[x]^2*(f[x]^2 + Derivative[1][f][x]) - 3*f[x]*y[x]*Derivative[1][y][x] + Derivative[1][y][x]^2, y[x], x]
Maple ✗
cpu = 2.203 (sec), leaf count = 0 , could not solve
dsolve(2*y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2-3*f(x)*y(x)*diff(y(x),x)-2*(diff(f(x),x)+f(x)^2)*y(x)^2+8*y(x)^3, y(x),'implicit')
Mathematica raw input
DSolve[2*y[x]*y''[x] == 8*y[x]^3 - 2*y[x]^2*(f[x]^2 + f'[x]) - 3*f[x]*y[x]*y'[x] + y'[x]^2,y[x],x]
Mathematica raw output
DSolve[2*y[x]*Derivative[2][y][x] == 8*y[x]^3 - 2*y[x]^2*(f[x]^2 + Derivative[1][f][x]) - 3*f[x]*y[x]*Derivative[1][y][x] + Derivative[1][y][x]^2, y[x], x]
Maple raw input
dsolve(2*y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2-3*f(x)*y(x)*diff(y(x),x)-2*(diff(f(x),x)+f(x)^2)*y(x)^2+8*y(x)^3, y(x),'implicit')
Maple raw output
dsolve(2*y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2-3*f(x)*y(x)*diff(y(x),x)-2*(diff(f(x),x)+f(x)^2)*y(x)^2+8*y(x)^3, y(x),'implicit')