65.2.9 problem 8 a(ii)

Internal problem ID [15628]
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(ii)
Date solved : Thursday, October 02, 2025 at 10:21:23 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 (1\right )&=3 \\ y^{\prime }\left (1\right )&=-1 \\ \end{align*}

✓ Maple. Time used: 0.058 (sec). Leaf size: 21

ode:=diff(diff(y(x),x),x)-diff(y(x),x)-2*y(x) = 0; 
ic:=[y(1) = 3, D(y)(1) = -1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {2 \,{\mathrm e}^{-2+2 x}}{3}+\frac {7 \,{\mathrm e}^{1-x}}{3} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 28

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

\begin{align*} y(x)&\to \frac {7 e^{1-x}}{3}+\frac {2}{3} e^{2 x-2} \end{align*}

✓ Sympy. Time used: 0.100 (sec). Leaf size: 24

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(1): 3, Subs(Derivative(y(x), x), x, 1): -1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {2 e^{2 x}}{3 e^{2}} + \frac {7 e e^{- x}}{3} \]