Internal problem ID [3927]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 7
Problem number: First order with homogeneous Coefficients. Exercise 7.10, page
61.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {2 y \,{\mathrm e}^{\frac {x}{y}}+\left (y-2 x \,{\mathrm e}^{\frac {x}{y}}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.116 (sec). Leaf size: 23
dsolve(2*y(x)*exp(x/y(x))+(y(x)-2*x*exp(x/y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {x}{\RootOf \left (\frac {\textit {\_Z} \,{\mathrm e}^{-2 \,{\mathrm e}^{\textit {\_Z}}}}{c_{1}}-x \right )} \]
✓ Solution by Mathematica
Time used: 0.256 (sec). Leaf size: 29
DSolve[2*y[x]*Exp[x/y[x]]+(y[x]-2*x*Exp[x/y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-2 e^{\frac {x}{y(x)}}-\log \left (\frac {y(x)}{x}\right )=\log (x)+c_1,y(x)\right ] \]