##### 4.20.6 $$y(x) y'(x)^2+\left (x-y(x)^2\right ) y'(x)-x y(x)=0$$

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

[_quadrature]

Book solution method
No Missing Variables ODE, Solve for $$y'$$

Mathematica
cpu = 0.170458 (sec), leaf count = 49

$\left \{\left \{y(x)\to c_1 e^x\right \},\left \{y(x)\to -\sqrt {-x^2+2 c_1}\right \},\left \{y(x)\to \sqrt {-x^2+2 c_1}\right \}\right \}$

Maple
cpu = 0.053 (sec), leaf count = 34

$\left [y \left (x \right ) = \sqrt {-x^{2}+\textit {\_C1}}, y \left (x \right ) = -\sqrt {-x^{2}+\textit {\_C1}}, y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{x}\right ]$ Mathematica raw input

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

Mathematica raw output

{{y[x] -> E^x*C[1]}, {y[x] -> -Sqrt[-x^2 + 2*C[1]]}, {y[x] -> Sqrt[-x^2 + 2*C[1]
]}}

Maple raw input

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

Maple raw output

[y(x) = (-x^2+_C1)^(1/2), y(x) = -(-x^2+_C1)^(1/2), y(x) = _C1*exp(x)]