\[ a \left (-\sqrt {y'(x)^2+1}\right )-b+y''(x)=0 \] ✓ Mathematica : cpu = 0.318829 (sec), leaf count = 414
\[\left \{\left \{y(x)\to \frac {a \text {InverseFunction}\left [\frac {\frac {b \tan ^{-1}\left (\frac {\text {$\#$1} b}{\sqrt {\text {$\#$1}^2+1} \sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}-\frac {b \tan ^{-1}\left (\frac {\text {$\#$1} a}{\sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}+\sinh ^{-1}(\text {$\#$1})}{a}\& \right ][x+c_1]{}^2-b \sqrt {1+\text {InverseFunction}\left [\frac {\frac {b \tan ^{-1}\left (\frac {\text {$\#$1} b}{\sqrt {\text {$\#$1}^2+1} \sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}-\frac {b \tan ^{-1}\left (\frac {\text {$\#$1} a}{\sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}+\sinh ^{-1}(\text {$\#$1})}{a}\& \right ][x+c_1]{}^2} \log \left (b+a \sqrt {1+\text {InverseFunction}\left [\frac {\frac {b \tan ^{-1}\left (\frac {\text {$\#$1} b}{\sqrt {\text {$\#$1}^2+1} \sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}-\frac {b \tan ^{-1}\left (\frac {\text {$\#$1} a}{\sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}+\sinh ^{-1}(\text {$\#$1})}{a}\& \right ][x+c_1]{}^2}\right )+a}{a^2 \sqrt {1+\text {InverseFunction}\left [\frac {\frac {b \tan ^{-1}\left (\frac {\text {$\#$1} b}{\sqrt {\text {$\#$1}^2+1} \sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}-\frac {b \tan ^{-1}\left (\frac {\text {$\#$1} a}{\sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}+\sinh ^{-1}(\text {$\#$1})}{a}\& \right ][x+c_1]{}^2}}+c_2\right \}\right \}\] ✓ Maple : cpu = 1.779 (sec), leaf count = 31
\[y \relax (x ) = \int \RootOf \left (x -\left (\int _{}^{\textit {\_Z}}\frac {1}{a \sqrt {\textit {\_f}^{2}+1}+b}d \textit {\_f} \right )+c_{1}\right )d x +c_{2}\]