Internal problem ID [960]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Existence and Uniqueness of Solutions of Nonlinear
Equations. Section 2.3 Page 60
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {y^{\prime }-\tan \left (x y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.064 (sec). Leaf size: 44
dsolve(diff(y(x),x)=tan(x*y(x)),y(x), singsol=all)
\[ y \relax (x ) = -i \RootOf \left (\sqrt {2}\, c_{1}-\erf \left (\frac {\left (-x +\textit {\_Z} \right ) \sqrt {2}}{2}\right ) \sqrt {\pi }-\erf \left (\frac {\sqrt {2}\, \left (x +\textit {\_Z} \right )}{2}\right ) \sqrt {\pi }\right ) \]
✓ Solution by Mathematica
Time used: 0.31 (sec). Leaf size: 69
DSolve[y'[x]==Tan[x*y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{2} \sqrt {\frac {\pi }{2}} e^{\frac {x^2}{2}} \left (\text {Erfi}\left (\frac {y(x)-i x}{\sqrt {2}}\right )+\text {Erfi}\left (\frac {y(x)+i x}{\sqrt {2}}\right )\right )=c_1 e^{\frac {x^2}{2}},y(x)\right ] \]