12.2.6 problem 6

Internal problem ID [1542]
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 : 6
Date solved : Monday, January 27, 2025 at 04:59:23 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

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

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

\[ y = \frac {{\mathrm e}^{1-x}}{x} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 16

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

\[ y(x)\to \frac {e^{1-x}}{x} \]