4.11.10 \(x^2+x y(x) y'(x)+y(x)^2=0\)

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 = 0.00717274 (sec), leaf count = 46

\[\left \{\left \{y(x)\to -\frac {\sqrt {c_1-\frac {x^4}{2}}}{x}\right \},\left \{y(x)\to \frac {\sqrt {c_1-\frac {x^4}{2}}}{x}\right \}\right \}\]

Maple
cpu = 0.006 (sec), leaf count = 19

\[ \left \{ \left (y \relax (x ) \right ) ^{2}+{\frac {{x}^{2}}{2}}-{\frac {{\it \_C1}}{{x}^{2}}}=0 \right \} \] Mathematica raw input

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

Mathematica raw output

{{y[x] -> -(Sqrt[-x^4/2 + C[1]]/x)}, {y[x] -> Sqrt[-x^4/2 + C[1]]/x}}

Maple raw input

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

Maple raw output

y(x)^2+1/2*x^2-1/x^2*_C1 = 0