Internal problem ID [4027]
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 12.15, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {2 y-x y \ln \left (x \right )-2 y^{\prime } x \ln \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve((2*y(x)-x*y(x)*ln(x))-2*x*ln(x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-\frac {x}{2}} \ln \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 22
DSolve[(2*y[x]-x*y[x]*Log[x])-2*x*Log[x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-x/2} \log (x) \\ y(x)\to 0 \\ \end{align*}