74.11.40 problem 52

Internal problem ID [16290]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 52
Date solved : Tuesday, January 28, 2025 at 09:00:39 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

With initial conditions

\begin{align*} y \left (0\right )&=-{\frac {5}{16}}\\ y^{\prime }\left (0\right )&={\frac {9}{16}} \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 15

dsolve([diff(y(t),t$2)+7*diff(y(t),t)+10*y(t)=t*exp(-t),y(0) = -5/16, D(y)(0) = 9/16],y(t), singsol=all)
 

\[ y = \frac {\left (4 t -5\right ) {\mathrm e}^{-t}}{16} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 19

DSolve[{D[y[t],{t,2}]+7*D[y[t],t]+10*y[t]==t*Exp[-t],{y[0]==-15/48,Derivative[1][y][0] ==9/16}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{16} e^{-t} (4 t-5) \]