ODE
\[ \left (a^2+x^2\right ) y'(x)+(x-y(x)) y(x)=0 \] ODE Classification
[_rational, _Bernoulli]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.456118 (sec), leaf count = 32
\[\left \{\left \{y(x)\to \frac {a^2}{-x+a^2 c_1 \sqrt {a^2+x^2}}\right \}\right \}\]
Maple ✓
cpu = 0.021 (sec), leaf count = 28
\[\left [y \left (x \right ) = \frac {a^{2}}{\sqrt {a^{2}+x^{2}}\, \textit {\_C1} \,a^{2}-x}\right ]\] Mathematica raw input
DSolve[(x - y[x])*y[x] + (a^2 + x^2)*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> a^2/(-x + a^2*Sqrt[a^2 + x^2]*C[1])}}
Maple raw input
dsolve((a^2+x^2)*diff(y(x),x)+(x-y(x))*y(x) = 0, y(x))
Maple raw output
[y(x) = a^2/((a^2+x^2)^(1/2)*_C1*a^2-x)]