26.7.24 problem Exercise 20.25, page 220

Internal problem ID [7074]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number : Exercise 20.25, page 220
Date solved : Tuesday, September 30, 2025 at 04:21:09 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+6 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 37

ode:=6*y(x)+5*diff(diff(y(x),x),x)+diff(diff(diff(diff(y(x),x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \sin \left (\sqrt {2}\, x \right )+c_2 \cos \left (\sqrt {2}\, x \right )+c_3 \sin \left (\sqrt {3}\, x \right )+c_4 \cos \left (\sqrt {3}\, x \right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 50

ode=D[y[x],{x,4}]+5*D[y[x],{x,2}]+6*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_3 \cos \left (\sqrt {2} x\right )+c_1 \cos \left (\sqrt {3} x\right )+c_4 \sin \left (\sqrt {2} x\right )+c_2 \sin \left (\sqrt {3} x\right ) \end{align*}

✓ Sympy. Time used: 0.050 (sec). Leaf size: 42

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*y(x) + 5*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \sin {\left (\sqrt {2} x \right )} + C_{2} \sin {\left (\sqrt {3} x \right )} + C_{3} \cos {\left (\sqrt {2} x \right )} + C_{4} \cos {\left (\sqrt {3} x \right )} \]