74.11.39 problem 51

Internal problem ID [16289]
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 : 51
Date solved : Tuesday, January 28, 2025 at 09:00:37 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+8 y^{\prime }+16 y&=4 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&={\frac {5}{4}}\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 17

dsolve([diff(y(t),t$2)+8*diff(y(t),t)+16*y(t)=4,y(0) = 5/4, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = {\mathrm e}^{-4 t}+4 t \,{\mathrm e}^{-4 t}+\frac {1}{4} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 20

DSolve[{D[y[t],{t,2}]+8*D[y[t],t]+16*y[t]==4,{y[0]==5/4,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

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