76.19.2 problem 2

Internal problem ID [17726]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 5. The Laplace transform. Section 5.4 (Solving differential equations with Laplace transform). Problems at page 327
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 11:01:54 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=t \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 9.806 (sec). Leaf size: 21

dsolve([diff(y(t),t$2)+3*diff(y(t),t)+2*y(t)=t,y(0) = 1, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = -\frac {5 \,{\mathrm e}^{-2 t}}{4}+\frac {t}{2}+3 \,{\mathrm e}^{-t}-\frac {3}{4} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 28

DSolve[{D[y[t],{t,2}]+3*D[y[t],t]+2*y[t]==t,{y[0]==1,Derivative[1][y][0] == 0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{4} \left (2 t-5 e^{-2 t}+12 e^{-t}-3\right ) \]