ODE
\[ x y(x) y'(x)+y(x)^2+1=0 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.262535 (sec), leaf count = 50
\[\left \{\left \{y(x)\to -\frac {\sqrt {-x^2+e^{2 c_1}}}{x}\right \},\left \{y(x)\to \frac {\sqrt {-x^2+e^{2 c_1}}}{x}\right \}\right \}\]
Maple ✓
cpu = 0.019 (sec), leaf count = 34
\[\left [y \left (x \right ) = \frac {\sqrt {-x^{2}+\textit {\_C1}}}{x}, y \left (x \right ) = -\frac {\sqrt {-x^{2}+\textit {\_C1}}}{x}\right ]\] 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))
Maple raw output
[y(x) = (-x^2+_C1)^(1/2)/x, y(x) = -(-x^2+_C1)^(1/2)/x]