Internal problem ID [8453]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 117.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {x y^{\prime }-x \,{\mathrm e}^{\frac {y}{x}}-y=x} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve(x*diff(y(x),x) - x*exp(y(x)/x) - y(x) - x=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (\ln \left (-\frac {x}{-1+x \,{\mathrm e}^{c_{1}}}\right )+c_{1} \right ) x \]
✓ Solution by Mathematica
Time used: 4.535 (sec). Leaf size: 38
DSolve[x*y'[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*}