67.12.3 problem 19.1 (c)

Internal problem ID [16642]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 19. Arbitrary Homogeneous linear equations with constant coefficients. Additional exercises page 369
Problem number : 19.1 (c)
Date solved : Thursday, October 02, 2025 at 01:37:19 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-34 y^{\prime \prime }+225 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 29

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-34*diff(diff(y(x),x),x)+225*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{10 x}+c_2 \,{\mathrm e}^{8 x}+c_3 \,{\mathrm e}^{2 x}+c_4 \right ) {\mathrm e}^{-5 x} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 39

ode=D[y[x],{x,4}]-34*D[y[x],{x,2}]+225*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-5 x} \left (e^{2 x} \left (c_3 e^{6 x}+c_4 e^{8 x}+c_2\right )+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.053 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(225*y(x) - 34*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 5 x} + C_{2} e^{- 3 x} + C_{3} e^{3 x} + C_{4} e^{5 x} \]