74.5.56 problem 63 (a)

Internal problem ID [16020]
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 (a)
Date solved : Tuesday, January 28, 2025 at 08:26:42 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 11

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

\[ y = -1+{\mathrm e}^{-t}+t \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 13

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

\[ y(t)\to t+e^{-t}-1 \]