2.557   ODE No. 557

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

✓ Mathematica : cpu = 0.0347759 (sec), leaf count = 39

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

\[\left \{\left \{y(x)\to -\sqrt {-x^2+c_1 x}\right \},\left \{y(x)\to \sqrt {-x^2+c_1 x}\right \}\right \}\]

✓ Maple : cpu = 0.076 (sec), leaf count = 105

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

\[y \left (x \right ) = \frac {x \left (\sqrt {-\frac {c_{1}^{2}}{x \left (-2 c_{1} +x \right )}}\, \sqrt {2 x c_{1} -x^{2}}+c_{1} -x \right )}{\sqrt {2 x c_{1} -x^{2}}}\]