76.2.1 problem 1

Internal problem ID [17337]
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 : 1
Date solved : Tuesday, January 28, 2025 at 10:01:38 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+4 y&=t +{\mathrm e}^{-2 t} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

dsolve(diff(y(t),t)+4*y(t)=t+exp(-2*t),y(t), singsol=all)
 

\[ y = \frac {t}{4}-\frac {1}{16}+\frac {{\mathrm e}^{-2 t}}{2}+{\mathrm e}^{-4 t} c_{1} \]

✓ Solution by Mathematica

Time used: 0.166 (sec). Leaf size: 37

DSolve[D[y[t],t]+4*y[t]==t+Exp[-2*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-4 t} \left (\int _1^t\left (e^{4 K[1]} K[1]+e^{2 K[1]}\right )dK[1]+c_1\right ) \]