60.1.210 problem 211

Internal problem ID [10224]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 211
Date solved : Monday, January 27, 2025 at 06:40:01 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 31

dsolve(y(x)*diff(y(x),x)-x*exp(x/y(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: 0.139 (sec). Leaf size: 41

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

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