10.1.3 problem 3

Internal problem ID [1100]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 3
Date solved : Monday, January 27, 2025 at 04:33:25 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y+y^{\prime }&=1+t \,{\mathrm e}^{-t} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

dsolve(y(t)+diff(y(t),t) = 1+t/exp(t),y(t), singsol=all)
 

\[ y = 1+\frac {\left (t^{2}+2 c_1 \right ) {\mathrm e}^{-t}}{2} \]

✓ Solution by Mathematica

Time used: 0.055 (sec). Leaf size: 27

DSolve[y[t]+D[y[t],t] == 1+t/Exp[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{2} e^{-t} \left (t^2+2 e^t+2 c_1\right ) \]