Internal problem ID [889]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } x +\ln \relax (x ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 13
dsolve(x*diff(y(x),x) + ln(x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-\frac {\ln \relax (x )^{2}}{2}} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 23
DSolve[x*y'[x] +Log[x]*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-\frac {1}{2} \log ^2(x)} \\ y(x)\to 0 \\ \end{align*}