10.6.6 problem 6

Internal problem ID [1223]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Miscellaneous problems, end of chapter 2. Page 133
Problem number : 6
Date solved : Monday, January 27, 2025 at 04:45:53 AM
CAS classification : [_linear]

\begin{align*} y x +x y^{\prime }&=1-y \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 20

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

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