4.21.42 \(-\left (x^3+x y(x)+y(x)^2\right ) y'(x)+y'(x)^3+x y(x) (y(x)+x)=0\)

ODE
\[ -\left (x^3+x y(x)+y(x)^2\right ) y'(x)+y'(x)^3+x y(x) (y(x)+x)=0 \] ODE Classification

[`y=_G(x,y')`]

Book solution method
No Missing Variables ODE, Solve for \(y'\)

Mathematica
cpu = 375.028 (sec), leaf count = 0 , could not solve

DSolve[x*y[x]*(x + y[x]) - (x^3 + x*y[x] + y[x]^2)*Derivative[1][y][x] + Derivative[1][y][x]^3 == 0, y[x], x]

Maple
cpu = 1.606 (sec), leaf count = 0 , could not solve

dsolve(diff(y(x),x)^3-(x^3+x*y(x)+y(x)^2)*diff(y(x),x)+(x+y(x))*x*y(x) = 0, y(x),'implicit')

Mathematica raw input

DSolve[x*y[x]*(x + y[x]) - (x^3 + x*y[x] + y[x]^2)*y'[x] + y'[x]^3 == 0,y[x],x]

Mathematica raw output

DSolve[x*y[x]*(x + y[x]) - (x^3 + x*y[x] + y[x]^2)*Derivative[1][y][x] + Derivat
ive[1][y][x]^3 == 0, y[x], x]

Maple raw input

dsolve(diff(y(x),x)^3-(x^3+x*y(x)+y(x)^2)*diff(y(x),x)+(x+y(x))*x*y(x) = 0, y(x),'implicit')

Maple raw output

dsolve(diff(y(x),x)^3-(x^3+x*y(x)+y(x)^2)*diff(y(x),x)+(x+y(x))*x*y(x) = 0, y(x)
,'implicit')