ODE
\[ y''(x)=a \sqrt {y'(x)^2+1} \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.299047 (sec), leaf count = 19
\[\left \{\left \{y(x)\to \frac {\cosh (a x+c_1)}{a}+c_2\right \}\right \}\]
Maple ✓
cpu = 2.063 (sec), leaf count = 18
\[\left [y \left (x \right ) = \frac {\cosh \left (\textit {\_C1} a +a x \right )}{a}+\textit {\_C2}\right ]\] Mathematica raw input
DSolve[y''[x] == a*Sqrt[1 + y'[x]^2],y[x],x]
Mathematica raw output
{{y[x] -> C[2] + Cosh[a*x + C[1]]/a}}
Maple raw input
dsolve(diff(diff(y(x),x),x) = a*(1+diff(y(x),x)^2)^(1/2), y(x))
Maple raw output
[y(x) = 1/a*cosh(_C1*a+a*x)+_C2]