74.10.25 problem 25

Internal problem ID [16230]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.2, page 147
Problem number : 25
Date solved : Tuesday, January 28, 2025 at 08:57:59 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 14

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

\[ y = {\mathrm e}^{-2 t} \left (5 t +1\right ) \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 16

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

\[ y(t)\to e^{-2 t} (5 t+1) \]