ODE
\[ 2 x (x+1) y(x) y'(x)=y(x)^2+1 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.0174176 (sec), leaf count = 58
\[\left \{\left \{y(x)\to -\frac {\sqrt {\left (e^{2 c_1}-1\right ) x-1}}{\sqrt {x+1}}\right \},\left \{y(x)\to \frac {\sqrt {\left (e^{2 c_1}-1\right ) x-1}}{\sqrt {x+1}}\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 23
\[ \left \{ {\frac { \left ( 1+x \right ) \left ( y \left ( x \right ) \right ) ^{2}-{\it \_C1}\,x+1}{1+x}}=0 \right \} \] Mathematica raw input
DSolve[2*x*(1 + x)*y[x]*y'[x] == 1 + y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> -(Sqrt[-1 + (-1 + E^(2*C[1]))*x]/Sqrt[1 + x])}, {y[x] -> Sqrt[-1 + (-1 + E^(2*C[1]))*x]/Sqrt[1 + x]}}
Maple raw input
dsolve(2*(1+x)*x*y(x)*diff(y(x),x) = 1+y(x)^2, y(x),'implicit')
Maple raw output
((1+x)*y(x)^2-_C1*x+1)/(1+x) = 0