ODE
\[ x y'(x)=y(x) \left (y(x)^2+1\right ) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.246914 (sec), leaf count = 59
\[\left \{\left \{y(x)\to -\frac {i e^{c_1} x}{\sqrt {-1+e^{2 c_1} x^2}}\right \},\left \{y(x)\to \frac {i e^{c_1} x}{\sqrt {-1+e^{2 c_1} x^2}}\right \}\right \}\]
Maple ✓
cpu = 0.017 (sec), leaf count = 30
\[\left [y \left (x \right ) = \frac {x}{\sqrt {-x^{2}+\textit {\_C1}}}, y \left (x \right ) = -\frac {x}{\sqrt {-x^{2}+\textit {\_C1}}}\right ]\] Mathematica raw input
DSolve[x*y'[x] == y[x]*(1 + y[x]^2),y[x],x]
Mathematica raw output
{{y[x] -> ((-I)*E^C[1]*x)/Sqrt[-1 + E^(2*C[1])*x^2]}, {y[x] -> (I*E^C[1]*x)/Sqrt[-1 + E^(2*C[1])*x^2]}}
Maple raw input
dsolve(x*diff(y(x),x) = y(x)*(1+y(x)^2), y(x))
Maple raw output
[y(x) = 1/(-x^2+_C1)^(1/2)*x, y(x) = -1/(-x^2+_C1)^(1/2)*x]