Internal problem ID [5604]
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: 10.
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: 0.015 (sec). Leaf size: 31
dsolve(diff(y(x),x$4)+2*a^2*diff(y(x),x$2)+a^4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sin \left (a x \right )+c_{2} \cos \left (a x \right )+c_{3} \sin \left (a x \right ) x +c_{4} \cos \left (a x \right ) x \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 30
DSolve[y''''[x]+2*a^2*y''[x]+a^4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (c_2 x+c_1) \cos (a x)+(c_4 x+c_3) \sin (a x) \\ \end{align*}