18.11 problem section 9.2, problem 11

Internal problem ID [1475]

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.
ODE order: 4.
ODE degree: 1.

CAS Maple gives this as type [[_high_order, _missing_x]]

Solve \begin {gather*} \boxed {16 y^{\prime \prime \prime \prime }-72 y^{\prime \prime }+81 y=0} \end {gather*}

Solution by Maple

Time used: 0.003 (sec). Leaf size: 31

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

\[ y \relax (x ) = c_{1} {\mathrm e}^{-\frac {3 x}{2}}+c_{2} {\mathrm e}^{-\frac {3 x}{2}} x +c_{3} {\mathrm e}^{\frac {3 x}{2}}+c_{4} {\mathrm e}^{\frac {3 x}{2}} x \]

Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 33

DSolve[16*y''''[x]-72*y''[x]+81*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to e^{-3 x/2} \left (c_2 x+e^{3 x} (c_4 x+c_3)+c_1\right ) \\ \end{align*}