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 = 0.00833812 (sec), leaf count = 60

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

Maple
cpu = 0.005 (sec), leaf count = 19

\[ \left \{ \left (y \relax (x ) \right ) ^{2}+{\frac {{x}^{2}}{3}}-{\frac {{\it \_C1}}{x}}=0 \right \} \] 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),'implicit')

Maple raw output

y(x)^2+1/3*x^2-1/x*_C1 = 0