##### 4.11.45 $$x^2+2 x y(x) y'(x)+y(x)^2=0$$

ODE
$x^2+2 x y(x) y'(x)+y(x)^2=0$ ODE Classiﬁcation

[[_homogeneous, class A], _exact, _rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.298272 (sec), leaf count = 60

$\left \{\left \{y(x)\to -\frac {\sqrt {-x^3+3 c_1}}{\sqrt {3} \sqrt {x}}\right \},\left \{y(x)\to \frac {\sqrt {-x^3+3 c_1}}{\sqrt {3} \sqrt {x}}\right \}\right \}$

Maple
cpu = 0.02 (sec), leaf count = 49

$\left [y \left (x \right ) = -\frac {\sqrt {3}\, \sqrt {x \left (-x^{3}+3 \textit {\_C1} \right )}}{3 x}, y \left (x \right ) = \frac {\sqrt {3}\, \sqrt {x \left (-x^{3}+3 \textit {\_C1} \right )}}{3 x}\right ]$ Mathematica raw input

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

[y(x) = -1/3/x*3^(1/2)*(x*(-x^3+3*_C1))^(1/2), y(x) = 1/3/x*3^(1/2)*(x*(-x^3+3*_
C1))^(1/2)]