74.9.5 problem 13

Internal problem ID [16102]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.1, page 141
Problem number : 13
Date solved : Thursday, March 13, 2025 at 07:51:46 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=-5 \end{align*}

✓ Maple. Time used: 0.018 (sec). Leaf size: 15

ode:=diff(diff(y(t),t),t)-diff(y(t),t)-2*y(t) = 0; 
ic:=y(0) = -1, D(y)(0) = -5; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = {\mathrm e}^{-t}-2 \,{\mathrm e}^{2 t} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 18

ode=D[y[t],{t,2}]-D[y[t],t]-2*y[t]==0; 
ic={y[0]==-1,Derivative[1][y][0] ==-5}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.148 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-2*y(t) - Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): -1, Subs(Derivative(y(t), t), t, 0): -5} 
dsolve(ode,func=y(t),ics=ics)
 

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