\[ \sqrt {a^2+x^2} y'(x)-\sqrt {a^2+x^2}+y(x)+x=0 \] ✓ Mathematica : cpu = 631.94 (sec), leaf count = 167
\[\left \{\left \{y(x)\to \frac {\sqrt {1-\frac {x}{\sqrt {a^2+x^2}}} \int _1^x \frac {\sqrt {\frac {K[1]}{\sqrt {K[1]^2+a^2}}+1} \left (\sqrt {K[1]^2+a^2}-K[1]\right )}{\sqrt {K[1]^2+a^2} \sqrt {1-\frac {K[1]}{\sqrt {K[1]^2+a^2}}}} \, dK[1]}{\sqrt {\frac {x}{\sqrt {a^2+x^2}}+1}}+\frac {c_1 \sqrt {1-\frac {x}{\sqrt {a^2+x^2}}}}{\sqrt {\frac {x}{\sqrt {a^2+x^2}}+1}}\right \}\right \}\] ✓ Maple : cpu = 0.018 (sec), leaf count = 36
\[ \left \{ y \left ( x \right ) ={1 \left ( {a}^{2}\ln \left ( x+\sqrt {{a}^{2}+{x}^{2}} \right ) +{\it \_C1} \right ) \left ( x+\sqrt {{a}^{2}+{x}^{2}} \right ) ^{-1}} \right \} \]