\[ a \left (-\sqrt {y'(x)^2+1}\right )-b+y''(x)=0 \] ✓ Mathematica : cpu = 0.27744 (sec), leaf count = 414
\[\left \{\left \{y(x)\to \frac {a \text {InverseFunction}\left [\frac {\frac {b \tan ^{-1}\left (\frac {\text {$\#$1} b}{\sqrt {\text {$\#$1}^2+1} \sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}-\frac {b \tan ^{-1}\left (\frac {\text {$\#$1} a}{\sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}+\sinh ^{-1}(\text {$\#$1})}{a}\& \right ]\left [c_1+x\right ]{}^2-b \sqrt {\text {InverseFunction}\left [\frac {\frac {b \tan ^{-1}\left (\frac {\text {$\#$1} b}{\sqrt {\text {$\#$1}^2+1} \sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}-\frac {b \tan ^{-1}\left (\frac {\text {$\#$1} a}{\sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}+\sinh ^{-1}(\text {$\#$1})}{a}\& \right ]\left [c_1+x\right ]{}^2+1} \log \left (a \sqrt {\text {InverseFunction}\left [\frac {\frac {b \tan ^{-1}\left (\frac {\text {$\#$1} b}{\sqrt {\text {$\#$1}^2+1} \sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}-\frac {b \tan ^{-1}\left (\frac {\text {$\#$1} a}{\sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}+\sinh ^{-1}(\text {$\#$1})}{a}\& \right ]\left [c_1+x\right ]{}^2+1}+b\right )+a}{a^2 \sqrt {\text {InverseFunction}\left [\frac {\frac {b \tan ^{-1}\left (\frac {\text {$\#$1} b}{\sqrt {\text {$\#$1}^2+1} \sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}-\frac {b \tan ^{-1}\left (\frac {\text {$\#$1} a}{\sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}+\sinh ^{-1}(\text {$\#$1})}{a}\& \right ]\left [c_1+x\right ]{}^2+1}}+c_2\right \}\right \}\] ✓ Maple : cpu = 0.207 (sec), leaf count = 31
\[ \left \{ y \left ( x \right ) =\int \!{\it RootOf} \left ( x-\int ^{{\it \_Z}}\! \left ( a\sqrt {{{\it \_f}}^{2}+1}+b \right ) ^{-1}{d{\it \_f}}+{\it \_C1} \right ) \,{\rm d}x+{\it \_C2} \right \} \]