12.4.3 problem 3

Internal problem ID [1610]
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
Date solved : Tuesday, January 28, 2025 at 02:35:47 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }&=\tan \left (y x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.049 (sec). Leaf size: 43

dsolve(diff(y(x),x)=tan(x*y(x)),y(x), singsol=all)
 

\[ y = -i \operatorname {RootOf}\left (-\operatorname {erf}\left (\frac {\left (-x +\textit {\_Z} \right ) \sqrt {2}}{2}\right ) \sqrt {\pi }-\sqrt {\pi }\, \operatorname {erf}\left (\frac {\sqrt {2}\, \left (x +\textit {\_Z} \right )}{2}\right )+\sqrt {2}\, c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.277 (sec). Leaf size: 69

DSolve[D[y[x],x]==Tan[x*y[x]],y[x],x,IncludeSingularSolutions -> True]
 

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