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 = 328.961 (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 = 1.611 (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))
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] + Derivative[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))
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))