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

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

\[ \left \{ {\frac {x}{x+y \relax (x ) }}-\ln \relax (x ) -{\it \_C1}=0 \right \} \] 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