67.3.16 problem Problem 17

Internal problem ID [13955]
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 : Wednesday, March 05, 2025 at 10:24:12 PM
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*}

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

ode:=3*diff(diff(y(t),t),t)+8*diff(y(t),t)-3*y(t) = 0; 
ic:=y(0) = 3, D(y)(0) = -4; 
dsolve([ode,ic],y(t),method='laplace');
 

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

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

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

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

✓ Sympy. Time used: 0.183 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-3*y(t) + 8*Derivative(y(t), t) + 3*Derivative(y(t), (t, 2)),0) 
ics = {y(0): 3, Subs(Derivative(y(t), t), t, 0): -4} 
dsolve(ode,func=y(t),ics=ics)
 

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