60.1.116 problem 117

Internal problem ID [10130]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 117
Date solved : Monday, January 27, 2025 at 06:29:04 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 4.441 (sec). Leaf size: 38

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

\begin{align*} y(x)\to x \log \left (\frac {1}{2} \left (-1+\tanh \left (\frac {1}{2} (-\log (x)-c_1)\right )\right )\right ) \\ y(x)\to i \pi x \\ \end{align*}