12.18.11 problem section 9.2, problem 11

Internal problem ID [2125]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient. Page 483
Problem number : section 9.2, problem 11
Date solved : Tuesday, March 04, 2025 at 01:50:35 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 16 y^{\prime \prime \prime \prime }-72 y^{\prime \prime }+81 y&=0 \end{align*}

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

ode:=16*diff(diff(diff(diff(y(x),x),x),x),x)-72*diff(diff(y(x),x),x)+81*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_4 x +c_3 \right ) {\mathrm e}^{-\frac {3 x}{2}}+{\mathrm e}^{\frac {3 x}{2}} \left (c_2 x +c_1 \right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 37

ode=16*D[y[x],{x,4}]-72*D[y[x],{x,2}]+81*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-3 x/2} \left (c_3 e^{3 x}+x \left (c_4 e^{3 x}+c_2\right )+c_1\right ) \]

✓ Sympy. Time used: 0.100 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(81*y(x) - 72*Derivative(y(x), (x, 2)) + 16*Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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