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 : Wednesday, February 05, 2025 at 04:51:16 AM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

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

dsolve(6*diff(y(x),x$4)+11*diff(y(x),x$2)+4*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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