ODE
\[ x y(x) y'(x)+y(x)^2+1=0 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.0117978 (sec), leaf count = 50
\[\left \{\left \{y(x)\to -\frac {\sqrt {e^{2 c_1}-x^2}}{x}\right \},\left \{y(x)\to \frac {\sqrt {e^{2 c_1}-x^2}}{x}\right \}\right \}\]
Maple ✓
cpu = 0.006 (sec), leaf count = 15
\[ \left \{ 1-{\frac {{\it \_C1}}{{x}^{2}}}+ \left ( y \left ( x \right ) \right ) ^{2}=0 \right \} \] Mathematica raw input
DSolve[1 + y[x]^2 + x*y[x]*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(Sqrt[E^(2*C[1]) - x^2]/x)}, {y[x] -> Sqrt[E^(2*C[1]) - x^2]/x}}
Maple raw input
dsolve(x*y(x)*diff(y(x),x)+1+y(x)^2 = 0, y(x),'implicit')
Maple raw output
1-1/x^2*_C1+y(x)^2 = 0