76.24.4 problem Ex. 4

Internal problem ID [20155]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. problems at page 65
Problem number : Ex. 4
Date solved : Thursday, October 02, 2025 at 05:33:46 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 9 y^{\prime \prime }+18 y^{\prime }-16 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=9*diff(diff(y(x),x),x)+18*diff(y(x),x)-16*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_2 \,{\mathrm e}^{\frac {10 x}{3}}+c_1 \right ) {\mathrm e}^{-\frac {8 x}{3}} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 26

ode=9*D[y[x],{x,2}]+18*D[y[x],x]-16*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{-8 x/3}+c_2 e^{2 x/3} \end{align*}

✓ Sympy. Time used: 0.091 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-16*y(x) + 18*Derivative(y(x), x) + 9*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- \frac {8 x}{3}} + C_{2} e^{\frac {2 x}{3}} \]