Internal problem ID [892]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {\left (x +1\right ) y}{x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 14
dsolve([diff(y(x),x) + ((1+x)/x)*y(x)=0,y(1) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{1-x}}{x} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 16
DSolve[{y'[x] +((1+x)/x)*y[x]==0,y[1]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{1-x}}{x} \\ \end{align*}