10.6.26 problem 26

Internal problem ID [1243]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Miscellaneous problems, end of chapter 2. Page 133
Problem number : 26
Date solved : Monday, January 27, 2025 at 04:47:21 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

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

dsolve(x*diff(y(x),x) = exp(y(x)/x)*x+y(x),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*D[y[x],x] == Exp[y[x]/x]*x+y[x],y[x],x,IncludeSingularSolutions -> True]
 

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