29.8.8 problem 213

Internal problem ID [4813]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 213
Date solved : Monday, January 27, 2025 at 09:40:44 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.337 (sec). Leaf size: 18

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

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