74.5.43 problem 50

Internal problem ID [16007]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 50
Date solved : Tuesday, January 28, 2025 at 08:26:20 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

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

\[ y = 2-\frac {{\mathrm e}^{2 t}}{3}+{\mathrm e}^{-t} c_{1} \]

✓ Solution by Mathematica

Time used: 0.180 (sec). Leaf size: 24

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

\[ y(t)\to -\frac {e^{2 t}}{3}+c_1 e^{-t}+2 \]