65.2.11 problem 8 b(ii)

Internal problem ID [15630]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises 1.3, page 27
Problem number : 8 b(ii)
Date solved : Thursday, October 02, 2025 at 10:21:24 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 )&=0 \\ y^{\prime }\left (2\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.069 (sec). Leaf size: 25

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

\[ y = \frac {-{\mathrm e}^{-x}+{\mathrm e}^{2 x}}{2 \,{\mathrm e}^{4}+{\mathrm e}^{-2}} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 29

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

\begin{align*} y(x)&\to \frac {e^{2-x} \left (e^{3 x}-1\right )}{1+2 e^6} \end{align*}

✓ Sympy. Time used: 0.094 (sec). Leaf size: 31

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): 0, Subs(Derivative(y(x), x), x, 2): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {e^{2} e^{2 x}}{1 + 2 e^{6}} - \frac {e^{2} e^{- x}}{1 + 2 e^{6}} \]