\[ \sqrt {a^2+x^2} y'(x)-\sqrt {a^2+x^2}+y(x)+x=0 \] ✓ Mathematica : cpu = 4.07833 (sec), leaf count = 103
DSolve[x - Sqrt[a^2 + x^2] + y[x] + Sqrt[a^2 + x^2]*Derivative[1][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {1}{2} \left (x-\sqrt {a^2+x^2}\right ) \left (\log \left (1-\frac {x}{\sqrt {a^2+x^2}}\right )-\log \left (\frac {x}{\sqrt {a^2+x^2}}+1\right )\right )+\frac {c_1 \sqrt {1-\frac {x}{\sqrt {a^2+x^2}}}}{\sqrt {\frac {x}{\sqrt {a^2+x^2}}+1}}\right \}\right \}\] ✓ Maple : cpu = 0.014 (sec), leaf count = 36
dsolve((a^2+x^2)^(1/2)*diff(y(x),x)+y(x)-(a^2+x^2)^(1/2)+x = 0,y(x))
\[y \left (x \right ) = \frac {a^{2} \ln \left (x +\sqrt {a^{2}+x^{2}}\right )+c_{1}}{x +\sqrt {a^{2}+x^{2}}}\]