ODE
\[ y(x) y'(x)=\sqrt {y(x)^2-a^2} \] ODE Classification
[_quadrature]
Book solution method
Separable ODE, Independent variable missing
Mathematica ✓
cpu = 0.266027 (sec), leaf count = 39
\[\left \{\left \{y(x)\to -\sqrt {a^2+(x+c_1){}^2}\right \},\left \{y(x)\to \sqrt {a^2+(x+c_1){}^2}\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 29
\[\left [x +\frac {\left (a -y \left (x \right )\right ) \left (a +y \left (x \right )\right )}{\sqrt {y \left (x \right )^{2}-a^{2}}}+\textit {\_C1} = 0\right ]\] Mathematica raw input
DSolve[y[x]*y'[x] == Sqrt[-a^2 + y[x]^2],y[x],x]
Mathematica raw output
{{y[x] -> -Sqrt[a^2 + (x + C[1])^2]}, {y[x] -> Sqrt[a^2 + (x + C[1])^2]}}
Maple raw input
dsolve(y(x)*diff(y(x),x) = (y(x)^2-a^2)^(1/2), y(x))
Maple raw output
[x+(a-y(x))*(a+y(x))/(y(x)^2-a^2)^(1/2)+_C1 = 0]