12.18.7 problem section 9.2, problem 7

Internal problem ID [2121]
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 7
Date solved : Monday, January 27, 2025 at 05:42:38 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 27 y^{\prime \prime \prime }+27 y^{\prime \prime }+9 y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(27*diff(y(x),x$3)+27*diff(y(x),x$2)+9*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 25

DSolve[27*D[y[x],{x,3}]+27*D[y[x],{x,2}]+9*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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