2.83   ODE No. 83

\[ y'(x)-\tan (x y(x))=0 \]

✓ Mathematica : cpu = 0.270574 (sec), leaf count = 69

DSolve[-Tan[x*y[x]] + Derivative[1][y][x] == 0,y[x],x]
 

\[\text {Solve}\left [\frac {1}{2} \sqrt {\frac {\pi }{2}} e^{\frac {x^2}{2}} \left (\text {erfi}\left (\frac {y(x)-i x}{\sqrt {2}}\right )+\text {erfi}\left (\frac {y(x)+i x}{\sqrt {2}}\right )\right )=c_1 e^{\frac {x^2}{2}},y(x)\right ]\]

✓ Maple : cpu = 0.477 (sec), leaf count = 44

dsolve(diff(y(x),x)-tan(x*y(x)) = 0,y(x))
 

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