ODE
\[ x y'(x)+y(x)=a \left (x^2+1\right ) y(x)^3 \] ODE Classification
[_rational, _Bernoulli]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.269855 (sec), leaf count = 51
\[\left \{\left \{y(x)\to -\frac {1}{\sqrt {-2 a x^2 \log (x)+a+c_1 x^2}}\right \},\left \{y(x)\to \frac {1}{\sqrt {-2 a x^2 \log (x)+a+c_1 x^2}}\right \}\right \}\]
Maple ✓
cpu = 0.024 (sec), leaf count = 43
\[\left [y \left (x \right ) = \frac {1}{\sqrt {-2 \ln \left (x \right ) x^{2} a +x^{2} \textit {\_C1} +a}}, y \left (x \right ) = -\frac {1}{\sqrt {-2 \ln \left (x \right ) x^{2} a +x^{2} \textit {\_C1} +a}}\right ]\] Mathematica raw input
DSolve[y[x] + x*y'[x] == a*(1 + x^2)*y[x]^3,y[x],x]
Mathematica raw output
{{y[x] -> -(1/Sqrt[a + x^2*C[1] - 2*a*x^2*Log[x]])}, {y[x] -> 1/Sqrt[a + x^2*C[1] - 2*a*x^2*Log[x]]}}
Maple raw input
dsolve(x*diff(y(x),x)+y(x) = a*(x^2+1)*y(x)^3, y(x))
Maple raw output
[y(x) = 1/(-2*ln(x)*x^2*a+x^2*_C1+a)^(1/2), y(x) = -1/(-2*ln(x)*x^2*a+x^2*_C1+a)^(1/2)]