ODE
\[ x y'(x)=\sqrt {a^2-x^2} \] ODE Classification
[_quadrature]
Book solution method
Separable ODE, Dependent variable missing
Mathematica ✓
cpu = 0.154 (sec), leaf count = 42
\[\left \{\left \{y(x)\to \sqrt {a^2-x^2}-a \tanh ^{-1}\left (\frac {\sqrt {a^2-x^2}}{a}\right )+c_1\right \}\right \}\]
Maple ✓
cpu = 0.023 (sec), leaf count = 56
\[\left [y \left (x \right ) = \sqrt {a^{2}-x^{2}}-\frac {a^{2} \ln \left (\frac {2 a^{2}+2 \sqrt {a^{2}}\, \sqrt {a^{2}-x^{2}}}{x}\right )}{\sqrt {a^{2}}}+\textit {\_C1}\right ]\] Mathematica raw input
DSolve[x*y'[x] == Sqrt[a^2 - x^2],y[x],x]
Mathematica raw output
{{y[x] -> Sqrt[a^2 - x^2] - a*ArcTanh[Sqrt[a^2 - x^2]/a] + C[1]}}
Maple raw input
dsolve(x*diff(y(x),x) = (a^2-x^2)^(1/2), y(x))
Maple raw output
[y(x) = (a^2-x^2)^(1/2)-a^2/(a^2)^(1/2)*ln((2*a^2+2*(a^2)^(1/2)*(a^2-x^2)^(1/2))/x)+_C1]