12.18.1 problem section 9.2, problem 1

Internal problem ID [2115]
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 1
Date solved : Monday, January 27, 2025 at 05:42:35 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 21

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

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