10.8.8 problem 14

Internal problem ID [1280]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.3 Complex Roots of the Characteristic Equation , page 164
Problem number : 14
Date solved : Tuesday, March 04, 2025 at 12:27:37 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 9 y^{\prime \prime }+9 y^{\prime }-4 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

ode:=9*diff(diff(y(x),x),x)+9*diff(y(x),x)-4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_2 \,{\mathrm e}^{\frac {5 x}{3}}+c_1 \right ) {\mathrm e}^{-\frac {4 x}{3}} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 26

ode=9*D[y[x],{x,2}]+9*D[y[x],x]-4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-4 x/3} \left (c_2 e^{5 x/3}+c_1\right ) \]

✓ Sympy. Time used: 0.153 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*y(x) + 9*Derivative(y(x), x) + 9*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- \frac {4 x}{3}} + C_{2} e^{\frac {x}{3}} \]