7.19.14 problem 40

Internal problem ID [554]
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 : 40
Date solved : Wednesday, February 05, 2025 at 03:45:48 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+\frac {2 x^{\prime }}{5}+\frac {226 x}{25}&=6 \,{\mathrm e}^{-\frac {t}{5}} \cos \left (3 t \right ) \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.264 (sec). Leaf size: 14

dsolve([diff(x(t),t$2)+4/10*diff(x(t),t)+904/100*x(t)=6*exp(-t/5)*cos(3*t),x(0) = 0, D(x)(0) = 0],x(t), singsol=all)
 

\[ x \left (t \right ) = {\mathrm e}^{-\frac {t}{5}} \sin \left (3 t \right ) t \]

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 24

DSolve[{D[x[t],{t,2}]+4/10*D[x[t],t]+904/100*x[t]==6*Exp[-t/5]*Cos[3*t],{x[0]==0,Derivative[1][x][0] ==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to e^{-t/5} t \sin (t) (2 \cos (2 t)+1) \]