52.5.5 problem 35

Internal problem ID [8328]
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. 7.2.2 TRANSFORMS OF DERIVATIVES Page 289
Problem number : 35
Date solved : Monday, January 27, 2025 at 03:49:05 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+5 y^{\prime }+4 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.651 (sec). Leaf size: 17

dsolve([diff(y(t),t$2)+5*diff(y(t),t)+4*y(t)=0,y(0) = 1, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = \frac {4 \,{\mathrm e}^{-t}}{3}-\frac {{\mathrm e}^{-4 t}}{3} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 23

DSolve[{D[y[t],{t,2}]+5*D[y[t],t]+4*y[t]==0,{y[0]==1,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{3} e^{-4 t} \left (4 e^{3 t}-1\right ) \]