4.17.6 \(-2 x^2 y'(x)+2 x y'(x)+y'(x)^2=0\)

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

[_quadrature]

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

Mathematica
cpu = 0.00402702 (sec), leaf count = 26

\[\left \{\left \{y(x)\to c_1\right \},\left \{y(x)\to c_1+\frac {2 x^3}{3}-x^2\right \}\right \}\]

Maple
cpu = 0.007 (sec), leaf count = 20

\[ \left \{ y \relax (x ) ={\it \_C1},y \relax (x ) ={\frac {2\,{x}^{3}}{3}}-{x}^{2}+{\it \_C1} \right \} \] Mathematica raw input

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

Mathematica raw output

{{y[x] -> C[1]}, {y[x] -> -x^2 + (2*x^3)/3 + C[1]}}

Maple raw input

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

Maple raw output

y(x) = 2/3*x^3-x^2+_C1, y(x) = _C1