12.18.11 problem section 9.2, problem 11

Internal problem ID [2125]
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 11
Date solved : Monday, January 27, 2025 at 05:42:39 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 16 y^{\prime \prime \prime \prime }-72 y^{\prime \prime }+81 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 25

dsolve(16*diff(y(x),x$4)-72*diff(y(x),x$2)+81*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_4 x +c_3 \right ) {\mathrm e}^{-\frac {3 x}{2}}+{\mathrm e}^{\frac {3 x}{2}} \left (c_2 x +c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 37

DSolve[16*D[y[x],{x,4}]-72*D[y[x],{x,2}]+81*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x/2} \left (c_3 e^{3 x}+x \left (c_4 e^{3 x}+c_2\right )+c_1\right ) \]