\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -a\sqrt { \left ( y \left ( x \right ) \right ) ^{2}+1}-b=0} \]
Mathematica: cpu = 0.176522 (sec), leaf count = 96 \[ \left \{\left \{y(x)\to \text {InverseFunction}\left [\frac {\frac {b \tan ^{-1}\left (\frac {\text {$\#$1} b}{\sqrt {\text {$\#$1}^2+1} \sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}-\frac {b \tan ^{-1}\left (\frac {\text {$\#$1} a}{\sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}+\sinh ^{-1}(\text {$\#$1})}{a}\& \right ]\left [c_1+x\right ]\right \}\right \} \]
Maple: cpu = 0.032 (sec), leaf count = 26 \[ \left \{ x-\int ^{y \left ( x \right ) }\! \left ( a\sqrt {{{\it \_a}}^{2 }+1}+b \right ) ^{-1}{d{\it \_a}}+{\it \_C1}=0 \right \} \]
Sage: cpu = 0 (sec), leaf count = 0 \[ \text {Maxima was unable to solve this ODE} \]