9.2.8 problem problem 17

Internal problem ID [942]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Section 5.3, Higher-Order Linear Differential Equations. Homogeneous Equations with Constant Coefficients. Page 300
Problem number : problem 17
Date solved : Tuesday, March 04, 2025 at 12:06:15 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 6 y^{\prime \prime \prime \prime }+11 y^{\prime \prime }+4 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 41

ode:=6*diff(diff(diff(diff(y(x),x),x),x),x)+11*diff(diff(y(x),x),x)+4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 94

ode=D[y[x],{x,4}]+11*D[y[x],{x,2}]+4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_3 \cos \left (\sqrt {\frac {1}{2} \left (11-\sqrt {105}\right )} x\right )+c_1 \cos \left (\sqrt {\frac {1}{2} \left (11+\sqrt {105}\right )} x\right )+c_4 \sin \left (\sqrt {\frac {1}{2} \left (11-\sqrt {105}\right )} x\right )+c_2 \sin \left (\sqrt {\frac {1}{2} \left (11+\sqrt {105}\right )} x\right ) \]

✓ Sympy. Time used: 0.098 (sec). Leaf size: 53

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) + 11*Derivative(y(x), (x, 2)) + 6*Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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