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 = 0.0168714 (sec), leaf count = 32
\[\left \{\left \{y(x)\to \frac {a^2}{a^2 c_1 \sqrt {a^2+x^2}-x}\right \}\right \}\]
Maple ✓
cpu = 0.009 (sec), leaf count = 25
\[ \left \{ {\frac {x}{{a}^{2}}}-\sqrt {{a}^{2}+{x}^{2}}{\it \_C1}+ \left ( y \left ( x \right ) \right ) ^{-1}=0 \right \} \] 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),'implicit')
Maple raw output
1/a^2*x-(a^2+x^2)^(1/2)*_C1+1/y(x) = 0