9.2.7 problem problem 16

Internal problem ID [941]
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 16
Date solved : Wednesday, February 05, 2025 at 04:51:15 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 25

dsolve(diff(y(x),x$4)+18*diff(y(x),x$2)+81*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_4 x +c_2 \right ) \cos \left (3 x \right )+\sin \left (3 x \right ) \left (x c_3 +c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 30

DSolve[D[y[x],{x,4}]+18*D[y[x],{x,2}]+81*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (c_2 x+c_1) \cos (3 x)+(c_4 x+c_3) \sin (3 x) \]