ODE
\[ x^2 y'(x)+x^2+x y(x)+y(x)^2=0 \] ODE Classification
[[_homogeneous, `class A`], _rational, _Riccati]
Book solution method
Homogeneous equation
Mathematica ✓
cpu = 0.0108986 (sec), leaf count = 24
\[\left \{\left \{y(x)\to \frac {x \left (-c_1+\log (x)-1\right )}{c_1-\log (x)}\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 19
\[ \left \{ {\frac {x}{x+y \left ( x \right ) }}-\ln \left ( x \right ) -{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[x^2 + x*y[x] + y[x]^2 + x^2*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (x*(-1 - C[1] + Log[x]))/(C[1] - Log[x])}}
Maple raw input
dsolve(x^2*diff(y(x),x)+x^2+x*y(x)+y(x)^2 = 0, y(x),'implicit')
Maple raw output
x/(x+y(x))-ln(x)-_C1 = 0