Internal problem ID [5471]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y \tan \left (\frac {y}{x}\right )}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 27
dsolve(diff(y(x),x)=y(x)/x*tan(y(x)/x),y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (-\left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a} \left (\tan \left (\textit {\_a} \right )-1\right )}d \textit {\_a} \right )+\ln \relax (x )+c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 1.838 (sec). Leaf size: 33
DSolve[y'[x]==y[x]/x*Tan[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{K[1] (\tan (K[1])-1)}dK[1]=\log (x)+c_1,y(x)\right ] \]