76.18.2 problem 13

Internal problem ID [17713]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 5. The Laplace transform. Section 5.2 (Properties of the Laplace transform). Problems at page 309
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 11:01:44 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 9 y^{\prime \prime }+12 y^{\prime }+4 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 10.723 (sec). Leaf size: 13

dsolve([9*diff(y(t),t$2)+12*diff(y(t),t)+4*y(t)=0,y(0) = 2, D(y)(0) = -1],y(t), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-\frac {2 t}{3}} \left (t +6\right )}{3} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 19

DSolve[{9*D[y[t],{t,2}]+12*D[y[t],t]+4*y[t]==0,{y[0]==2,Derivative[1][y][0] == -1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{3} e^{-2 t/3} (t+6) \]