Internal problem ID [450]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.1. Page 40
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y+y^{\prime }-1-t \,{\mathrm e}^{-t}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(y(t)+diff(y(t),t) = 1+t/exp(t),y(t), singsol=all)
\[ y \relax (t ) = \left (\frac {t^{2}}{2}+{\mathrm e}^{t}+c_{1}\right ) {\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 23
DSolve[y[t]+y'[t] == 1+t/Exp[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 1+e^{-t} \left (\frac {t^2}{2}+c_1\right ) \\ \end{align*}