50.4.8 problem 8

Internal problem ID [7857]
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 1.5. Exact Equations. Page 20
Problem number : 8
Date solved : Monday, January 27, 2025 at 03:27:09 PM
CAS classification : [_separable]

\begin{align*} -\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 13

dsolve(-1/y(x)*sin(x/y(x))+(x/y(x)^2*sin(x/y(x)))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {x}{\pi -c_{1}} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 19

DSolve[-1/y[x]*Sin[x/y[x]]+(x/y[x]^2*Sin[x/y[x]])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 x \\ y(x)\to \text {ComplexInfinity} \\ y(x)\to \text {ComplexInfinity} \\ \end{align*}