13.12 problem 12

Internal problem ID [5606]

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: 12.
ODE order: 4.
ODE degree: 1.

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

Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }+5 y=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 30

dsolve(diff(y(x),x$4)+2*diff(y(x),x$3)-2*diff(y(x),x$2)-6*diff(y(x),x)+5*y(x)=0,y(x), singsol=all)
 

\[ y \relax (x ) = c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{x} x +c_{3} \sin \relax (x ) {\mathrm e}^{-2 x}+c_{4} \cos \relax (x ) {\mathrm e}^{-2 x} \]

Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 34

DSolve[y''''[x]+2*y'''[x]-2*y''[x]-6*y'[x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to e^x (c_4 x+c_3)+e^{-2 x} (c_2 \cos (x)+c_1 \sin (x)) \\ \end{align*}