ODE
\[ y'(x)^3+\left (2 x-y(x)^2\right ) y'(x)^2-2 x y(x)^2 y'(x)=0 \] ODE Classification
[_quadrature]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.0092636 (sec), leaf count = 31
\[\left \{\left \{y(x)\to -\frac {1}{c_1+x}\right \},\left \{y(x)\to c_1\right \},\left \{y(x)\to c_1-x^2\right \}\right \}\]
Maple ✓
cpu = 0.008 (sec), leaf count = 26
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{-1}+x-{\it \_C1}=0,y \left ( x \right ) ={\it \_C1},y \left ( x \right ) =-{x}^{2}+{\it \_C1} \right \} \] Mathematica raw input
DSolve[-2*x*y[x]^2*y'[x] + (2*x - y[x]^2)*y'[x]^2 + y'[x]^3 == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(x + C[1])^(-1)}, {y[x] -> C[1]}, {y[x] -> -x^2 + C[1]}}
Maple raw input
dsolve(diff(y(x),x)^3+(2*x-y(x)^2)*diff(y(x),x)^2-2*x*y(x)^2*diff(y(x),x) = 0, y(x),'implicit')
Maple raw output
1/y(x)+x-_C1 = 0, y(x) = -x^2+_C1, y(x) = _C1