2.336   ODE No. 336

\[ \left (a x+\sqrt {y(x)^2+1}\right ) y'(x)+a y(x)+\sqrt {x^2+1}=0 \] Mathematica : cpu = 0.281508 (sec), leaf count = 53


\[\text {Solve}\left [a x y(x)+\frac {1}{2} \sqrt {x^2+1} x+\frac {1}{2} \left (y(x) \sqrt {y(x)^2+1}+\sinh ^{-1}(y(x))\right )+\frac {1}{2} \sinh ^{-1}(x)=c_1,y(x)\right ]\] Maple : cpu = 0.039 (sec), leaf count = 41


\[\frac {x \sqrt {x^{2}+1}}{2}+\frac {\arcsinh \relax (x )}{2}+a x y \relax (x )+\frac {y \relax (x ) \sqrt {y \relax (x )^{2}+1}}{2}+\frac {\arcsinh \left (y \relax (x )\right )}{2}+c_{1} = 0\]