73.11.17 problem 17.3 (e)

Internal problem ID [15252]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 17. Second order Homogeneous equations with constant coefficients. Additional exercises page 334
Problem number : 17.3 (e)
Date solved : Thursday, March 13, 2025 at 05:50:49 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 16 y^{\prime \prime }-24 y^{\prime }+9 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 14

ode:=16*diff(diff(y(x),x),x)-24*diff(y(x),x)+9*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 20

ode=16*D[y[x],{x,2}]-24*D[y[x],x]+9*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.155 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) - 24*Derivative(y(x), x) + 16*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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