39.5.15 problem Problem 24.44

Internal problem ID [6557]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 24. Solutions of linear DE by Laplace transforms. Supplementary Problems. page 248
Problem number : Problem 24.44
Date solved : Monday, January 27, 2025 at 02:12:14 PM
CAS classification : [[_2nd_order, _missing_x]]

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

Using Laplace method With initial conditions

\begin{align*} x \left (0\right )&=2\\ x^{\prime }\left (0\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 0.171 (sec). Leaf size: 13

dsolve([diff(x(t),t$2)+4*diff(x(t),t)+4*x(t)=0,x(0) = 2, D(x)(0) = -2],x(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 47

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

\[ x(t)\to \frac {2}{7} e^{-3 t/2} \left (\sqrt {7} \sin \left (\frac {\sqrt {7} t}{2}\right )+7 \cos \left (\frac {\sqrt {7} t}{2}\right )\right ) \]