77.9.5 problem 5

Internal problem ID [20448]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter III. Ordinary linear differential equations with constant coefficients. Exercise III(A) at page 31
Problem number : 5
Date solved : Thursday, October 02, 2025 at 06:03:00 PM
CAS classification : [[_2nd_order, _missing_x]]

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

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

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

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

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 26

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

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

✓ Sympy. Time used: 0.092 (sec). Leaf size: 19

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

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