2.59   ODE No. 59

\[ a \left (-\sqrt {y(x)^2+1}\right )-b+y'(x)=0 \]

✓ Mathematica : cpu = 0.249474 (sec), leaf count = 84

DSolve[-b - a*Sqrt[1 + y[x]^2] + Derivative[1][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\frac {\frac {2 b \tan ^{-1}\left (\frac {\left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right ) a+b}{\sqrt {a^2-b^2}}\right )}{\sqrt {a^2-b^2}}-\log \left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right )}{a}\& \right ][x+c_1]\right \}\right \}\]

✓ Maple : cpu = 0.085 (sec), leaf count = 26

dsolve(diff(y(x),x)-a*(y(x)^2+1)^(1/2)-b = 0,y(x))
 

\[x -\left (\int _{}^{y \left (x \right )}\frac {1}{a \sqrt {\textit {\_a}^{2}+1}+b}d \textit {\_a} \right )+c_{1} = 0\]