15.9.14 problem 28

Internal problem ID [3071]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 17, page 78
Problem number : 28
Date solved : Monday, January 27, 2025 at 07:19:10 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime }+8 y&=0 \end{align*}

Solution by Maple

Time used: 0.003 (sec). Leaf size: 34

dsolve(diff(y(x),x$4)-6*diff(y(x),x$2)+8*y(x)=0,y(x), singsol=all)
 
\[ y = {\mathrm e}^{-2 x} c_{1} +{\mathrm e}^{2 x} c_2 +c_3 \,{\mathrm e}^{\sqrt {2}\, x}+c_4 \,{\mathrm e}^{-\sqrt {2}\, x} \]

Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 47

DSolve[D[y[x],{x,4}]-6*D[y[x],{x,2}]+8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 
\[ y(x)\to c_1 e^{\sqrt {2} x}+c_2 e^{-\sqrt {2} x}+c_3 e^{-2 x}+c_4 e^{2 x} \]