73.10.19 problem 15.7 (b)

Internal problem ID [15235]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 15. General solutions to Homogeneous linear differential equations. Additional exercises page 294
Problem number : 15.7 (b)
Date solved : Thursday, March 13, 2025 at 05:50:14 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-10 y^{\prime \prime }+9 y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 29

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-10*diff(diff(y(x),x),x)+9*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left ({\mathrm e}^{6 x} c_{2} +c_4 \,{\mathrm e}^{4 x}+c_{3} {\mathrm e}^{2 x}+c_{1} \right ) {\mathrm e}^{-3 x} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 36

ode=D[y[x],{x,4}]-10*D[y[x],{x,2}]+9*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.097 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) - 10*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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