7.19.1 problem 27

Internal problem ID [541]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 4. Laplace transform methods. Section 4.3 (Translation and partial fractions). Problems at page 296
Problem number : 27
Date solved : Wednesday, February 05, 2025 at 03:45:40 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+6 x^{\prime }+25 x&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} x \left (0\right )&=2\\ x^{\prime }\left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.206 (sec). Leaf size: 23

dsolve([diff(x(t),t$2)+6*diff(x(t),t)+25*x(t)=0,x(0) = 2, D(x)(0) = 3],x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {{\mathrm e}^{-3 t} \left (8 \cos \left (4 t \right )+9 \sin \left (4 t \right )\right )}{4} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 27

DSolve[{D[x[t],{t,2}]+6*D[x[t],t]+25*x[t]==0,{x[0]==2,Derivative[1][x][0] ==3}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{4} e^{-3 t} (9 \sin (4 t)+8 \cos (4 t)) \]