73.9.33 problem 14.5 (c)

Internal problem ID [15215]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 14. Higher order equations and the reduction of order method. Additional exercises page 277
Problem number : 14.5 (c)
Date solved : Thursday, March 13, 2025 at 05:49:36 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+24 y^{\prime \prime }-32 y^{\prime }+16 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 24

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-8*diff(diff(diff(y(x),x),x),x)+24*diff(diff(y(x),x),x)-32*diff(y(x),x)+16*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{2 x} \left (x^{3} c_4 +x^{2} c_{3} +c_{2} x +c_{1} \right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 28

ode=D[y[x],{x,4}]-8*D[y[x],{x,3}]+24*D[y[x],{x,2}]-32*D[y[x],x]+16*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{2 x} (x (x (c_4 x+c_3)+c_2)+c_1) \]

✓ Sympy. Time used: 0.216 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(16*y(x) - 32*Derivative(y(x), x) + 24*Derivative(y(x), (x, 2)) - 8*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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