Internal problem ID [4036]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous
Methods
Problem number: Exercise 12.23, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } x -x -y-{\mathrm e}^{\frac {y}{x}} x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 20
dsolve(x*diff(y(x),x)=x*exp(y(x)/x)+x+y(x),y(x), singsol=all)
\[ y \relax (x ) = \left (\ln \left (-\frac {x}{x \,{\mathrm e}^{c_{1}}-1}\right )+c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 3.639 (sec). Leaf size: 30
DSolve[x*y'[x]==x*Exp[y[x]/x]+x+y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \log \left (-1+\frac {1}{1+e^{c_1} x}\right ) \\ y(x)\to i \pi x \\ \end{align*}