4.11.8 \(x y(x) y'(x)+y(x)^2+1=0\)

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

\[ \left \{ 1-{\frac {{\it \_C1}}{{x}^{2}}}+ \left (y \relax (x ) \right ) ^{2}=0 \right \} \] 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