64.20.9 problem 9

Internal problem ID [13652]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 9, The Laplace transform. Section 9.3, Exercises page 452
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 05:54:21 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=4 t \,{\mathrm e}^{-3 t} \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 8.333 (sec). Leaf size: 19

dsolve([diff(y(t),t$2)+7*diff(y(t),t)+10*y(t)=4*t*exp(-3*t),y(0) = 0, D(y)(0) = -1],y(t), singsol=all)
 

\[ y = \left (-2 t -1\right ) {\mathrm e}^{-3 t}+{\mathrm e}^{-2 t} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 19

DSolve[{D[y[t],{t,2}]+7*D[y[t],t]+10*y[t]==4*t*Exp[-3*t],{y[0]==0,Derivative[1][y][0]==-1}},{y[t]},t,IncludeSingularSolutions -> True]
 

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