2.83   ODE No. 83

\[ y'(x)-\tan (x y(x))=0 \] Mathematica : cpu = 0.38866 (sec), leaf count = 69


\[\text {Solve}\left [\frac {1}{2} \sqrt {\frac {\pi }{2}} e^{\frac {x^2}{2}} \left (\text {erfi}\left (\frac {y(x)-i x}{\sqrt {2}}\right )+\text {erfi}\left (\frac {y(x)+i x}{\sqrt {2}}\right )\right )=c_1 e^{\frac {x^2}{2}},y(x)\right ]\] Maple : cpu = 0.374 (sec), leaf count = 44


\[y \relax (x ) = -i \RootOf \left (-\erf \left (\frac {\left (-x +\textit {\_Z} \right ) \sqrt {2}}{2}\right ) \sqrt {\pi }-\erf \left (\frac {\sqrt {2}\, \left (x +\textit {\_Z} \right )}{2}\right ) \sqrt {\pi }+\sqrt {2}\, c_{1}\right )\]