\[ a y(x) y''(x)+b y'(x)^2-\frac {y(x) y'(x)}{\sqrt {c^2+x^2}}=0 \] ✗ Mathematica : cpu = 3599.93 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 0.188 (sec), leaf count = 75
\[ \left \{ y \left ( x \right ) = \left ( \left ( {\frac {a}{a+b} \left ( {\frac {{\it \_C1}\,\sqrt [a]{2}a{x}^{{a}^{-1}+1}}{a+1}{\mbox {$_2$F$_1$}(-{\frac {1}{2\,a}},-{\frac {1}{2\,a}}-{\frac {1}{2}};\,1-{a}^{-1};\,-{\frac {{c}^{2}}{{x}^{2}}})}}+{\it \_C2} \right ) ^{-1}} \right ) ^{{\frac {a}{a+b}}} \right ) ^{-1} \right \} \]