Internal problem ID [7739]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 159.
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: 0.047 (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: 0.401 (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*}