71.2.8 problem 8 a(i)

Internal problem ID [14261]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises 1.3, page 27
Problem number : 8 a(i)
Date solved : Wednesday, March 05, 2025 at 10:41:47 PM
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 )&=2\\ y^{\prime }\left (0\right )&=-5 \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 17

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

\[ y = 3 \,{\mathrm e}^{-x}-{\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 19

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

\[ y(x)\to -e^{-x} \left (e^{3 x}-3\right ) \]

✓ Sympy. Time used: 0.151 (sec). Leaf size: 12

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

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