13.13 problem 13

Internal problem ID [5607]

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: 13.
ODE order: 3.
ODE degree: 1.

CAS Maple gives this as type [[_3rd_order, _missing_x]]

Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 21

dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+11*diff(y(x),x)-6*y(x)=0,y(x), singsol=all)
 

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

Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 25

DSolve[y'''[x]-6*y''[x]+11*y'[x]-6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to e^x \left (e^x \left (c_3 e^x+c_2\right )+c_1\right ) \\ \end{align*}