52.6.12 problem 32

Internal problem ID [8347]
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. 7.3.1 TRANSLATION ON THE s-AXIS. Page 297
Problem number : 32
Date solved : Monday, January 27, 2025 at 03:49:18 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+8 y^{\prime }+20 y&=0 \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.592 (sec). Leaf size: 5

dsolve([diff(y(t),t$2)+8*diff(y(t),t)+20*y(t)=0,y(0) = 0, D(y)(Pi) = 0],y(t), singsol=all)
 

\[ y = 0 \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 6

DSolve[{D[y[t],{t,2}]+8*D[y[t],t]+20*y[t]==0,{y[0]==0,Derivative[1][y][Pi]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 0 \]