15.2.17 problem 17

Internal problem ID [2887]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 6, page 25
Problem number : 17
Date solved : Monday, January 27, 2025 at 06:24:55 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.043 (sec). Leaf size: 15

dsolve([x*exp(y(x)/x)+y(x)=x*diff(y(x),x),y(1) = 0],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.337 (sec). Leaf size: 15

DSolve[{x*Exp[y[x]/x]+y[x]==x*D[y[x],x],y[1]==0},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -x \log (1-\log (x)) \]