ODE
\[ \left (a^2+x^2\right ) y'(x)+b x y(x)^2+x y(x)=0 \] ODE Classification
[_separable]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.354116 (sec), leaf count = 33
\[\left \{\left \{y(x)\to -\frac {e^{c_1}}{-\sqrt {a^2+x^2}+b e^{c_1}}\right \}\right \}\]
Maple ✓
cpu = 0.017 (sec), leaf count = 21
\[\left [y \left (x \right ) = \frac {1}{\sqrt {a^{2}+x^{2}}\, \textit {\_C1} -b}\right ]\] Mathematica raw input
DSolve[x*y[x] + b*x*y[x]^2 + (a^2 + x^2)*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(E^C[1]/(b*E^C[1] - Sqrt[a^2 + x^2]))}}
Maple raw input
dsolve((a^2+x^2)*diff(y(x),x)+x*y(x)+b*x*y(x)^2 = 0, y(x))
Maple raw output
[y(x) = 1/((a^2+x^2)^(1/2)*_C1-b)]