Internal problem ID [6221]
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]
\[ \boxed {y^{\prime }-\sin \left (\frac {y}{x}\right )+\cos \left (\frac {y}{x}\right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve(diff(y(x),x)=sin(y(x)/x)-cos(y(x)/x),y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {RootOf}\left (\int _{}^{\textit {\_Z}}\frac {1}{-\sin \left (\textit {\_a} \right )+\cos \left (\textit {\_a} \right )+\textit {\_a}}d \textit {\_a} +\ln \left (x \right )+c_{1} \right ) x \]
✓ Solution by Mathematica
Time used: 0.367 (sec). Leaf size: 36
DSolve[y'[x]==Sin[y[x]/x]-Cos[y[x]/x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{\cos (K[1])+K[1]-\sin (K[1])}dK[1]=-\log (x)+c_1,y(x)\right ] \]