Internal problem ID [4434]
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 7.9, page
61.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {y+x \ln \left (\frac {y}{x}\right ) y^{\prime }-2 x y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 18
dsolve(y(x)+x*ln(y(x)/x)*diff(y(x),x)-2*x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\operatorname {LambertW}\left (-{\mathrm e} x c_{1} \right )+1} x \]
✓ Solution by Mathematica
Time used: 5.502 (sec). Leaf size: 35
DSolve[y[x]+x*Log[y[x]/x]*y'[x]-2*x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -e^{c_1} W\left (-e^{1-c_1} x\right ) y(x)\to 0 y(x)\to e x \end{align*}