ODE
\[ y(x) y'(x)=\sqrt {a^2+y(x)^2} \] ODE Classification
[_quadrature]
Book solution method
Separable ODE, Independent variable missing
Mathematica ✓
cpu = 0.0143621 (sec), leaf count = 43
\[\left \{\left \{y(x)\to -\sqrt {\left (c_1+x\right ){}^2-a^2}\right \},\left \{y(x)\to \sqrt {\left (c_1+x\right ){}^2-a^2}\right \}\right \}\]
Maple ✓
cpu = 0.009 (sec), leaf count = 18
\[ \left \{ x-\sqrt { \left ( y \left ( x \right ) \right ) ^{2}+{a}^{2}}+{\it \_C1}=0 \right \} \] 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),'implicit')
Maple raw output
x-(y(x)^2+a^2)^(1/2)+_C1 = 0