62.3.1 problem Ex 1

Internal problem ID [12807]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 10. Homogeneous equations. Page 15
Problem number : Ex 1
Date solved : Tuesday, January 28, 2025 at 04:22:08 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 15

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

\[ y = \ln \left (-\frac {1}{\ln \left (x \right )+c_{1}}\right ) x \]

✓ Solution by Mathematica

Time used: 0.317 (sec). Leaf size: 18

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

\[ y(x)\to -x \log (-\log (x)-c_1) \]