67.3.5 problem Problem 6

Internal problem ID [13944]
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 6
Date solved : Wednesday, March 05, 2025 at 10:24:03 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-y^{\prime }-6 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*}

✓ Maple. Time used: 8.913 (sec). Leaf size: 15

ode:=diff(diff(y(t),t),t)-diff(y(t),t)-6*y(t) = 0; 
ic:=y(0) = 2, D(y)(0) = 1; 
dsolve([ode,ic],y(t),method='laplace');
 

\[ y = \left ({\mathrm e}^{5 t}+1\right ) {\mathrm e}^{-2 t} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 16

ode=D[y[t],{t,2}]-D[y[t],t]-6*y[t]==0; 
ic={y[0]==2,Derivative[1][y][0] ==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.175 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-6*y(t) - Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 2, Subs(Derivative(y(t), t), t, 0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

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