Internal problem ID [5004]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems.
page 12
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {x y^{\prime }-y \cos \left (\frac {y}{x}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(x*diff(y(x),x)=y(x)*cos(y(x)/x),y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (-\left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a} \left (\cos \left (\textit {\_a} \right )-1\right )}d \textit {\_a} \right )+\ln \relax (x )+c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 3.371 (sec). Leaf size: 33
DSolve[x*y'[x]==y[x]*Cos[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{(\cos (K[1])-1) K[1]}dK[1]=\log (x)+c_1,y(x)\right ] \]