2.337   ODE No. 337

\[ \left (\sqrt {x^2+y(x)^2}+x\right ) y'(x)-y(x)=0 \] Mathematica : cpu = 0.225766 (sec), leaf count = 161


\[\left \{\left \{y(x)\to -\sqrt {-2 i x \cosh (c_1)-2 i x \sinh (c_1)-\cosh (2 c_1)-\sinh (2 c_1)}\right \},\left \{y(x)\to \sqrt {-2 i x \cosh (c_1)-2 i x \sinh (c_1)-\cosh (2 c_1)-\sinh (2 c_1)}\right \},\left \{y(x)\to -\sqrt {2 i x \cosh (c_1)+2 i x \sinh (c_1)-\cosh (2 c_1)-\sinh (2 c_1)}\right \},\left \{y(x)\to \sqrt {2 i x \cosh (c_1)+2 i x \sinh (c_1)-\cosh (2 c_1)-\sinh (2 c_1)}\right \}\right \}\] Maple : cpu = 0.079 (sec), leaf count = 28


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