74.5.59 problem 63 (d)

Internal problem ID [16023]
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 : 63 (d)
Date solved : Tuesday, January 28, 2025 at 08:26:48 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 15

dsolve([diff(y(t),t)+y(t)=exp(t),y(0) = 0],y(t), singsol=all)
 

\[ y = \frac {{\mathrm e}^{t}}{2}-\frac {{\mathrm e}^{-t}}{2} \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 21

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

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