12.2.3 problem 3

Internal problem ID [1539]
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
Date solved : Monday, January 27, 2025 at 04:59:17 AM
CAS classification : [_separable]

\begin{align*} x y^{\prime }+y \ln \left (x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 13

dsolve(x*diff(y(x),x) + ln(x)*y(x)=0,y(x), singsol=all)
 

\[ y = c_1 \,{\mathrm e}^{-\frac {\ln \left (x \right )^{2}}{2}} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 23

DSolve[x*D[y[x],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*}