73.9.31 problem 14.5 (a)

Internal problem ID [15292]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 14. Higher order equations and the reduction of order method. Additional exercises page 277
Problem number : 14.5 (a)
Date solved : Tuesday, January 28, 2025 at 07:51:39 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

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

\[ y = {\mathrm e}^{3 x} \left (x^{2} c_{3} +c_{2} x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 23

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

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