4.39.46 \(2 y(x) y''(x)=y'(x)^2+4 (2 y(x)+x) y(x)^2\)

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

[NONE]

Book solution method
TO DO

Mathematica
cpu = 1.47049 (sec), leaf count = 0 , could not solve

DSolve[2*y[x]*Derivative[2][y][x] == 4*y[x]^2*(x + 2*y[x]) + Derivative[1][y][x]^2, y[x], x]

Maple
cpu = 0.227 (sec), leaf count = 0 , could not solve

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

Mathematica raw input

DSolve[2*y[x]*y''[x] == 4*y[x]^2*(x + 2*y[x]) + y'[x]^2,y[x],x]

Mathematica raw output

DSolve[2*y[x]*Derivative[2][y][x] == 4*y[x]^2*(x + 2*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*(x+2*y(x))*y(x)^2, y(x),'implicit')

Maple raw output

dsolve(2*y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2+4*(x+2*y(x))*y(x)^2, y(x),'i
mplicit')