50.5.22 problem 7(d)

Internal problem ID [7892]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.7. Homogeneous Equations. Page 28
Problem number : 7(d)
Date solved : Monday, January 27, 2025 at 03:31:25 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 27

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

\[ y = \operatorname {RootOf}\left (\ln \left (x \right )+c_{1} -\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a} \left (-1+\tan \left (\textit {\_a} \right )\right )}d \textit {\_a} \right ) x \]

✓ Solution by Mathematica

Time used: 1.429 (sec). Leaf size: 33

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{K[1] (\tan (K[1])-1)}dK[1]=\log (x)+c_1,y(x)\right ] \]