Internal problem ID [4048]
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 12.35, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x^{2}-1\right ) y^{\prime }-2 x y \ln \relax (y)=0} \end {gather*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 13
dsolve((x^2-1)*diff(y(x),x)-2*x*y(x)*ln(y(x))=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{c_{1} \left (x +1\right ) \left (x -1\right )} \]
✓ Solution by Mathematica
Time used: 0.348 (sec). Leaf size: 22
DSolve[(x^2-1)*y'[x]-2*x*y[x]*Log[y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{e^{c_1} \left (x^2-1\right )} \\ y(x)\to 1 \\ \end{align*}