Internal problem ID [5603]
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: 9.
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 a^{2} y^{\prime \prime }+a^{4} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 33
dsolve(diff(y(x),x$4)-2*a^2*diff(y(x),x$2)+a^4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{a x}+c_{2} {\mathrm e}^{a x} x +c_{3} {\mathrm e}^{-a x}+c_{4} {\mathrm e}^{-a x} x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 33
DSolve[y''''[x]-2*a^2*y''[x]+a^4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-a x} (c_2 x+c_1)+e^{a x} (c_4 x+c_3) \\ \end{align*}