78.12.24 problem 2 (f)

Internal problem ID [18240]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 17. The Homogeneous Equation with Constant Coefficients. Problems at page 125
Problem number : 2 (f)
Date solved : Monday, March 31, 2025 at 05:23:32 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+8 y^{\prime }-9 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2\\ y^{\prime }\left (1\right )&=0 \end{align*}

✓ Maple. Time used: 0.067 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)+8*diff(y(x),x)-9*y(x) = 0; 
ic:=y(1) = 2, D(y)(1) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {9 \,{\mathrm e}^{-1+x}}{5}+\frac {{\mathrm e}^{9-9 x}}{5} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 26

ode=D[y[x],{x,2}] +8*D[y[x],x]-9*y[x]==0; 
ic={y[1]==2,Derivative[1][y][1] == 0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{5} e^{9-9 x}+\frac {9 e^{x-1}}{5} \]

✓ Sympy. Time used: 0.173 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-9*y(x) + 8*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(1): 2, Subs(Derivative(y(x), x), x, 1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {9 e^{x}}{5 e} + \frac {e^{9} e^{- 9 x}}{5} \]