Internal problem ID [8420]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 83.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {y^{\prime }-\tan \left (x y\right )=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 44
dsolve(diff(y(x),x) - tan(x*y(x))=0,y(x), singsol=all)
\[ y \left (x \right ) = -i \operatorname {RootOf}\left (-\operatorname {erf}\left (\frac {\left (-x +\textit {\_Z} \right ) \sqrt {2}}{2}\right ) \sqrt {\pi }-\operatorname {erf}\left (\frac {\sqrt {2}\, \left (x +\textit {\_Z} \right )}{2}\right ) \sqrt {\pi }+c_{1} \sqrt {2}\right ) \]
✓ Solution by Mathematica
Time used: 0.283 (sec). Leaf size: 69
DSolve[y'[x] - Tan[x*y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{2} \sqrt {\frac {\pi }{2}} e^{\frac {x^2}{2}} \left (\text {erfi}\left (\frac {y(x)-i x}{\sqrt {2}}\right )+\text {erfi}\left (\frac {y(x)+i x}{\sqrt {2}}\right )\right )=c_1 e^{\frac {x^2}{2}},y(x)\right ] \]