\[ a \left (-\sqrt {y'(x)^2+1}\right )-b+y''(x)=0 \] ✓ Mathematica : cpu = 0.381115 (sec), leaf count = 972
DSolve[-b - a*Sqrt[1 + Derivative[1][y][x]^2] + Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_2-\frac {-\frac {2 a \text {InverseFunction}\left [\frac {\frac {2 b \arctan \left (\frac {b+a \left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right )}{\sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}-\log \left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right )}{a}\& \right ][x+c_1]{}^2}{\sqrt {\text {InverseFunction}\left [\frac {\frac {2 b \arctan \left (\frac {b+a \left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right )}{\sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}-\log \left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right )}{a}\& \right ][x+c_1]{}^2+1}}+b \log \left (\text {InverseFunction}\left [\frac {\frac {2 b \arctan \left (\frac {b+a \left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right )}{\sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}-\log \left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right )}{a}\& \right ][x+c_1]{}^2 a^2+a^2-b^2\right )+b \log \left (\frac {2 a^2 \left (a-i \sqrt {a^2-b^2} \text {InverseFunction}\left [\frac {\frac {2 b \arctan \left (\frac {b+a \left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right )}{\sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}-\log \left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right )}{a}\& \right ][x+c_1]+b \sqrt {\text {InverseFunction}\left [\frac {\frac {2 b \arctan \left (\frac {b+a \left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right )}{\sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}-\log \left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right )}{a}\& \right ][x+c_1]{}^2+1}\right )}{b^3 \left (a \text {InverseFunction}\left [\frac {\frac {2 b \arctan \left (\frac {b+a \left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right )}{\sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}-\log \left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right )}{a}\& \right ][x+c_1]+i \sqrt {a^2-b^2}\right )}\right )+b \log \left (\frac {2 a^2 \left (a+i \sqrt {a^2-b^2} \text {InverseFunction}\left [\frac {\frac {2 b \arctan \left (\frac {b+a \left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right )}{\sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}-\log \left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right )}{a}\& \right ][x+c_1]+b \sqrt {\text {InverseFunction}\left [\frac {\frac {2 b \arctan \left (\frac {b+a \left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right )}{\sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}-\log \left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right )}{a}\& \right ][x+c_1]{}^2+1}\right )}{b^3 \left (a \text {InverseFunction}\left [\frac {\frac {2 b \arctan \left (\frac {b+a \left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right )}{\sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}-\log \left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right )}{a}\& \right ][x+c_1]-i \sqrt {a^2-b^2}\right )}\right )-\frac {2 a}{\sqrt {\text {InverseFunction}\left [\frac {\frac {2 b \arctan \left (\frac {b+a \left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right )}{\sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}-\log \left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right )}{a}\& \right ][x+c_1]{}^2+1}}}{2 a^2}\right \}\right \}\] ✓ Maple : cpu = 0.154 (sec), leaf count = 31
dsolve(diff(diff(y(x),x),x)-a*(diff(y(x),x)^2+1)^(1/2)-b=0,y(x))
\[y \left (x \right ) = \int \operatorname {RootOf}\left (x -\left (\int _{}^{\textit {\_Z}}\frac {1}{a \sqrt {\textit {\_f}^{2}+1}+b}d \textit {\_f} \right )+c_{1}\right )d x +c_{2}\]