5.19 problem 7(a)

Internal problem ID [5468]

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(a).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]

Solve \begin {gather*} \boxed {y^{\prime }-\sin \left (\frac {y}{x}\right )+\cos \left (\frac {y}{x}\right )=0} \end {gather*}

Solution by Maple

Time used: 0.005 (sec). Leaf size: 29

dsolve(diff(y(x),x)=sin(y(x)/x)-cos(y(x)/x),y(x), singsol=all)
 

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

Solution by Mathematica

Time used: 0.219 (sec). Leaf size: 36

DSolve[y'[x]==Sin[y[x]/x]-Cos[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
 

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