ODE No. 555

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

✓ Mathematica : cpu = 0.0048813 (sec), leaf count = 20

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

\[\left \{\left \{y(x)\to c_1 x+\sqrt {1+c_1{}^2}\right \}\right \}\]

✓ Maple : cpu = 0.037 (sec), leaf count = 15

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

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