50.13.5 problem 5

Internal problem ID [8020]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Section 2.7. HIGHER ORDER LINEAR EQUATIONS, COUPLED HARMONIC OSCILLATORS Page 98
Problem number : 5
Date solved : Monday, January 27, 2025 at 03:36:52 PM
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: 19

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: 23

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]
 

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