74.5.26 problem 26

Internal problem ID [15990]
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 : 26
Date solved : Tuesday, January 28, 2025 at 08:25:50 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 11

dsolve([diff(y(t),t)-y(t)=4*exp(t),y(0) = 4],y(t), singsol=all)
 

\[ y = 4 \left (t +1\right ) {\mathrm e}^{t} \]

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 13

DSolve[{D[y[t],t]-y[t]==4*Exp[t],{y[0]==4}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 4 e^t (t+1) \]