76.2.3 problem 3

Internal problem ID [17339]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.2 (Linear equations: Method of integrating factors). Problems at page 54
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 10:01:42 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.060 (sec). Leaf size: 27

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

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