52.6.8 problem 28

Internal problem ID [8343]
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 : 28
Date solved : Monday, January 27, 2025 at 03:49:15 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime }+20 y^{\prime }+51 y&=0 \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.671 (sec). Leaf size: 30

dsolve([2*diff(y(t),t$2)+20*diff(y(t),t)+51*y(t)=0,y(0) = 2, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = 2 \,{\mathrm e}^{-5 t} \left (\cos \left (\frac {\sqrt {2}\, t}{2}\right )+5 \sqrt {2}\, \sin \left (\frac {\sqrt {2}\, t}{2}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 36

DSolve[{2*D[y[t],{t,2}]+20*D[y[t],t]+51*y[t]==0,{y[0]==2,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 2 e^{-5 t} \left (5 \sqrt {2} \sin \left (\frac {t}{\sqrt {2}}\right )+\cos \left (\frac {t}{\sqrt {2}}\right )\right ) \]