4.40.3 \(2 y(x) y''(x)=2 x f(x) y(x)^2-4 y(x)^2 y'(x)+y'(x)^2-y(x)^4-1\)

ODE
\[ 2 y(x) y''(x)=2 x f(x) y(x)^2-4 y(x)^2 y'(x)+y'(x)^2-y(x)^4-1 \] ODE Classification

[NONE]

Book solution method
TO DO

Mathematica
cpu = 0.0443155 (sec), leaf count = 0 , could not solve

DSolve[2*y[x]*Derivative[2][y][x] == -1 + 2*x*f[x]*y[x]^2 - y[x]^4 - 4*y[x]^2*Derivative[1][y][x] + Derivative[1][y][x]^2, y[x], x]

Maple
cpu = 0.386 (sec), leaf count = 0 , could not solve

dsolve(2*y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2-4*y(x)^2*diff(y(x),x)-1+2*f(x)*x*y(x)^2-y(x)^4, y(x),'implicit')

Mathematica raw input

DSolve[2*y[x]*y''[x] == -1 + 2*x*f[x]*y[x]^2 - y[x]^4 - 4*y[x]^2*y'[x] + y'[x]^2,y[x],x]

Mathematica raw output

DSolve[2*y[x]*Derivative[2][y][x] == -1 + 2*x*f[x]*y[x]^2 - y[x]^4 - 4*y[x]^2*De
rivative[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)^2-4*y(x)^2*diff(y(x),x)-1+2*f(x)*x*y(x)^2-y(x)^4, y(x),'implicit')

Maple raw output

dsolve(2*y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2-4*y(x)^2*diff(y(x),x)-1+2*f(
x)*x*y(x)^2-y(x)^4, y(x),'implicit')