52.8.14 problem 15(b)

Internal problem ID [8378]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 7 THE LAPLACE TRANSFORM. EXERCISES 7.5. Page 315
Problem number : 15(b)
Date solved : Monday, January 27, 2025 at 03:49:51 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=\delta \left (t \right ) \end{align*}

Using Laplace method

✓ Solution by Maple

Time used: 0.621 (sec). Leaf size: 30

dsolve(diff(y(t),t$2)+2*diff(y(t),t)+10*y(t)=Dirac(t),y(t), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-t} \left (3 y \left (0\right ) \cos \left (3 t \right )+\sin \left (3 t \right ) \left (y^{\prime }\left (0\right )+y \left (0\right )+1\right )\right )}{3} \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 38

DSolve[D[y[t],{t,2}]+2*D[y[t],t]+10*y[t]==DiracDelta[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{3} e^{-t} (\theta (t) \sin (3 t)+3 c_2 \cos (3 t)+3 c_1 \sin (3 t)) \]