70.13.19 problem 19

Internal problem ID [18888]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 19
Date solved : Thursday, October 02, 2025 at 03:32:30 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 25

ode:=diff(diff(y(x),x),x)-9*diff(y(x),x)+9*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{3 x \sqrt {5}}+c_2 \right ) {\mathrm e}^{-\frac {3 \left (\sqrt {5}-3\right ) x}{2}} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 36

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

\begin{align*} y(x)&\to e^{-\frac {3}{2} \left (\sqrt {5}-3\right ) x} \left (c_2 e^{3 \sqrt {5} x}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.104 (sec). Leaf size: 32

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

\[ y{\left (x \right )} = C_{1} e^{\frac {3 x \left (3 - \sqrt {5}\right )}{2}} + C_{2} e^{\frac {3 x \left (\sqrt {5} + 3\right )}{2}} \]