12.18.10 problem section 9.2, problem 10

Internal problem ID [2124]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient. Page 483
Problem number : section 9.2, problem 10
Date solved : Monday, January 27, 2025 at 05:42:39 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+12 y^{\prime \prime }+36 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 29

dsolve(diff(y(x),x$4)+12*diff(y(x),x$2)+36*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_4 x +c_2 \right ) \cos \left (x \sqrt {6}\right )+\sin \left (x \sqrt {6}\right ) \left (x c_3 +c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 38

DSolve[D[y[x],{x,4}]+12*D[y[x],{x,2}]+36*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (c_2 x+c_1) \cos \left (\sqrt {6} x\right )+(c_4 x+c_3) \sin \left (\sqrt {6} x\right ) \]