50.5.19 problem 7(a)

Internal problem ID [7889]
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)
Date solved : Monday, January 27, 2025 at 03:31:08 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 0.341 (sec). Leaf size: 36

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

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