4.5.42 \(2 x y'(x)+y(x) \left (y(x)^2+1\right )=0\)

ODE
\[ 2 x y'(x)+y(x) \left (y(x)^2+1\right )=0 \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.0176471 (sec), leaf count = 53

\[\left \{\left \{y(x)\to -\frac {i e^{c_1}}{\sqrt {e^{2 c_1}-x}}\right \},\left \{y(x)\to \frac {i e^{c_1}}{\sqrt {e^{2 c_1}-x}}\right \}\right \}\]

Maple
cpu = 0.005 (sec), leaf count = 13

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

DSolve[y[x]*(1 + y[x]^2) + 2*x*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> ((-I)*E^C[1])/Sqrt[E^(2*C[1]) - x]}, {y[x] -> (I*E^C[1])/Sqrt[E^(2*C[1
]) - x]}}

Maple raw input

dsolve(2*x*diff(y(x),x)+y(x)*(1+y(x)^2) = 0, y(x),'implicit')

Maple raw output

1-_C1*x+1/y(x)^2 = 0