64.20.4 problem 4

Internal problem ID [13568]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 9, The Laplace transform. Section 9.3, Exercises page 452
Problem number : 4
Date solved : Wednesday, March 05, 2025 at 10:03:53 PM
CAS classification : [[_2nd_order, _missing_x]]

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

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Maple. Time used: 8.394 (sec). Leaf size: 18

ode:=diff(diff(y(t),t),t)+diff(y(t),t)-12*y(t) = 0; 
ic:=y(0) = 4, D(y)(0) = -1; 
dsolve([ode,ic],y(t),method='laplace');
 

\[ y = \frac {\left (15 \,{\mathrm e}^{7 t}+13\right ) {\mathrm e}^{-4 t}}{7} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 23

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

\[ y(t)\to \frac {1}{7} e^{-4 t} \left (15 e^{7 t}+13\right ) \]

✓ Sympy. Time used: 0.152 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-12*y(t) + Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 4, Subs(Derivative(y(t), t), t, 0): -1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {15 e^{3 t}}{7} + \frac {13 e^{- 4 t}}{7} \]