\[ \sqrt {x^2+y(x)^2} y''(x)-a \left (y'(x)^2+1\right )^{3/2}=0 \] ✗ Mathematica : cpu = 300.064 (sec), leaf count = 0 , timed out
$Aborted
✗ Maple : cpu = 0. (sec), leaf count = 0 , could not solve
dsolve((y(x)^2+x^2)^(1/2)*diff(diff(y(x),x),x)-a*(diff(y(x),x)^2+1)^(3/2)=0,y(x))