76.18.4 problem 15

Internal problem ID [17715]
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 : 15
Date solved : Tuesday, January 28, 2025 at 11:01:45 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 6 y^{\prime \prime }+5 y^{\prime }+y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 10.599 (sec). Leaf size: 17

dsolve([6*diff(y(t),t$2)+5*diff(y(t),t)+y(t)=0,y(0) = 4, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = 12 \,{\mathrm e}^{-\frac {t}{3}}-8 \,{\mathrm e}^{-\frac {t}{2}} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 25

DSolve[{6*D[y[t],{t,2}]+5*D[y[t],t]+y[t]==0,{y[0]==4,Derivative[1][y][0] == 0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 4 e^{-t/2} \left (3 e^{t/6}-2\right ) \]