ODE
\[ 2 x y'(x)=y(x) \left (y(x)^2+1\right ) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.258518 (sec), leaf count = 63
\[\left \{\left \{y(x)\to -\frac {i e^{c_1} \sqrt {x}}{\sqrt {-1+e^{2 c_1} x}}\right \},\left \{y(x)\to \frac {i e^{c_1} \sqrt {x}}{\sqrt {-1+e^{2 c_1} x}}\right \}\right \}\]
Maple ✓
cpu = 0.016 (sec), leaf count = 42
\[\left [y \left (x \right ) = \frac {\sqrt {\left (-x +\textit {\_C1} \right ) x}}{-x +\textit {\_C1}}, y \left (x \right ) = -\frac {\sqrt {\left (-x +\textit {\_C1} \right ) x}}{-x +\textit {\_C1}}\right ]\] Mathematica raw input
DSolve[2*x*y'[x] == y[x]*(1 + y[x]^2),y[x],x]
Mathematica raw output
{{y[x] -> ((-I)*E^C[1]*Sqrt[x])/Sqrt[-1 + E^(2*C[1])*x]}, {y[x] -> (I*E^C[1]*Sqrt[x])/Sqrt[-1 + E^(2*C[1])*x]}}
Maple raw input
dsolve(2*x*diff(y(x),x) = y(x)*(1+y(x)^2), y(x))
Maple raw output
[y(x) = 1/(-x+_C1)*((-x+_C1)*x)^(1/2), y(x) = -1/(-x+_C1)*((-x+_C1)*x)^(1/2)]