67.3.16 problem Problem 17

Internal problem ID [14034]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 5.5 Laplace transform. Homogeneous equations. Problems page 357
Problem number : Problem 17
Date solved : Tuesday, January 28, 2025 at 06:13:04 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 3 y^{\prime \prime }+8 y^{\prime }-3 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-4 \end{align*}

✓ Solution by Maple

Time used: 9.049 (sec). Leaf size: 14

dsolve([3*diff(y(t),t$2)+8*diff(y(t),t)-3*y(t)=0,y(0) = 3, D(y)(0) = -4],y(t), singsol=all)
 

\[ y = 3 \,{\mathrm e}^{-\frac {4 t}{3}} \cosh \left (\frac {5 t}{3}\right ) \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 23

DSolve[{3*D[y[t],{t,2}]+8*D[y[t],t]-3*y[t]==0,{y[0]==3,Derivative[1][y][0] ==-4}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {3}{2} e^{-3 t} \left (e^{10 t/3}+1\right ) \]