Internal problem ID [1471]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {27 y^{\prime \prime \prime }+27 y^{\prime \prime }+9 y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
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)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-\frac {x}{3}}+c_{2} {\mathrm e}^{-\frac {x}{3}} x +c_{3} {\mathrm e}^{-\frac {x}{3}} x^{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 25
DSolve[27*y'''[x]+27*y''[x]+9*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x/3} (x (c_3 x+c_2)+c_1) \\ \end{align*}