50.5.20 problem 7(b)

Internal problem ID [7890]
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(b)
Date solved : Monday, January 27, 2025 at 03:31:13 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} {\mathrm e}^{\frac {x}{y}}-\frac {y y^{\prime }}{x}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 31

dsolve(exp(x/y(x))-y(x)/x*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \operatorname {RootOf}\left (-\int _{}^{\textit {\_Z}}\frac {\textit {\_a}}{-\textit {\_a}^{2}+{\mathrm e}^{\frac {1}{\textit {\_a}}}}d \textit {\_a} +\ln \left (x \right )+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.202 (sec). Leaf size: 41

DSolve[Exp[x/y[x]]-y[x]/x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {K[1]}{K[1]^2-e^{\frac {1}{K[1]}}}dK[1]=-\log (x)+c_1,y(x)\right ] \]