20.21.4 problem Problem 4

Internal problem ID [3931]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 10, The Laplace Transform and Some Elementary Applications. Exercises for 10.4. page 689
Problem number : Problem 4
Date solved : Monday, January 27, 2025 at 08:04:41 AM
CAS classification : [[_linear, `class A`]]

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

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 2.513 (sec). Leaf size: 15

dsolve([diff(y(t),t)+2*y(t)=4*t,y(0) = 1],y(t), singsol=all)
 

\[ y = 2 \,{\mathrm e}^{-2 t}+2 t -1 \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 17

DSolve[{D[y[t],t]+2*y[t]==4*t,{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 2 t+2 e^{-2 t}-1 \]