50.13.9 problem 9

Internal problem ID [8024]
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
Date solved : Monday, January 27, 2025 at 03:36:54 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 26

dsolve(diff(y(x),x$4)-2*a^2*diff(y(x),x$2)+a^4*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_4 x +c_3 \right ) {\mathrm e}^{-a x}+{\mathrm e}^{a x} \left (c_{2} x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 38

DSolve[D[y[x],{x,4}]-2*a^2*D[y[x],{x,2}]+a^4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-a x} \left (c_3 e^{2 a x}+x \left (c_4 e^{2 a x}+c_2\right )+c_1\right ) \]