ODE
\[ x^2+x y(x) y'(x)+y(x)^2=0 \] ODE Classification
[[_homogeneous, `class A`], _rational, _Bernoulli]
Book solution method
Homogeneous equation
Mathematica ✓
cpu = 0.269899 (sec), leaf count = 46
\[\left \{\left \{y(x)\to -\frac {\sqrt {-\frac {x^4}{2}+c_1}}{x}\right \},\left \{y(x)\to \frac {\sqrt {-\frac {x^4}{2}+c_1}}{x}\right \}\right \}\]
Maple ✓
cpu = 0.019 (sec), leaf count = 39
\[\left [y \left (x \right ) = -\frac {\sqrt {-2 x^{4}+4 \textit {\_C1}}}{2 x}, y \left (x \right ) = \frac {\sqrt {-2 x^{4}+4 \textit {\_C1}}}{2 x}\right ]\] Mathematica raw input
DSolve[x^2 + y[x]^2 + x*y[x]*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(Sqrt[-1/2*x^4 + C[1]]/x)}, {y[x] -> Sqrt[-1/2*x^4 + C[1]]/x}}
Maple raw input
dsolve(x*y(x)*diff(y(x),x)+x^2+y(x)^2 = 0, y(x))
Maple raw output
[y(x) = -1/2*(-2*x^4+4*_C1)^(1/2)/x, y(x) = 1/2*(-2*x^4+4*_C1)^(1/2)/x]