12.2.7 problem 7

Internal problem ID [1543]
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 : 7
Date solved : Monday, January 27, 2025 at 04:59:26 AM
CAS classification : [_separable]

\begin{align*} x y^{\prime }+\left (1+\frac {1}{\ln \left (x \right )}\right ) y&=0 \end{align*}

With initial conditions

\begin{align*} y \left ({\mathrm e}\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 14

dsolve([x*diff(y(x),x) + (1+1/ln(x))*y(x)=0,y(exp(1)) = 1],y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}}{x \ln \left (x \right )} \]

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 18

DSolve[{D[y[x],x] +(1+1/Log[x])*y[x]==0,y[Exp[1]]==1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-\operatorname {LogIntegral}(x)+\operatorname {LogIntegral}(e)-x+e} \]