Internal problem ID [573]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y x +y^{\prime } x -1+y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve([x*y(x)+x*diff(y(x),x) = 1-y(x),y(1) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {1-{\mathrm e}^{1-x}}{x} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 20
DSolve[{x*y[x]+x*y'[x] == 1-y[x],y[1]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e \sinh (x)-e \cosh (x)+1}{x} \\ \end{align*}