15.10.14 problem 14

Internal problem ID [3101]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 18, page 82
Problem number : 14
Date solved : Monday, January 27, 2025 at 07:19:28 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }-20 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 33

dsolve(diff(y(x),x$4)+diff(y(x),x$2)-20*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-2 x} c_{1} +{\mathrm e}^{2 x} c_2 +c_3 \sin \left (\sqrt {5}\, x \right )+c_4 \cos \left (\sqrt {5}\, x \right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 44

DSolve[D[y[x],{x,4}]+D[y[x],{x,2}]-20*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_3 e^{-2 x}+c_4 e^{2 x}+c_1 \cos \left (\sqrt {5} x\right )+c_2 \sin \left (\sqrt {5} x\right ) \]