9.2.6 problem problem 15

Internal problem ID [940]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Section 5.3, Higher-Order Linear Differential Equations. Homogeneous Equations with Constant Coefficients. Page 300
Problem number : problem 15
Date solved : Monday, January 27, 2025 at 03:22:36 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-16 y^{\prime \prime }+16 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 59

dsolve(diff(y(x),x$4)-16*diff(y(x),x$2)+16*y(x)=0,y(x), singsol=all)
 

\[ y = c_1 \,{\mathrm e}^{-\sqrt {2}\, \left (1+\sqrt {3}\right ) x}+c_2 \,{\mathrm e}^{\sqrt {2}\, \left (1+\sqrt {3}\right ) x}+c_3 \,{\mathrm e}^{-\sqrt {2}\, \left (\sqrt {3}-1\right ) x}+c_4 \,{\mathrm e}^{\sqrt {2}\, \left (\sqrt {3}-1\right ) x} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 86

DSolve[D[y[x],{x,4}]-16*D[y[x],{x,2}]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^{2 \sqrt {2-\sqrt {3}} x}+c_2 e^{-2 \sqrt {2-\sqrt {3}} x}+c_3 e^{2 \sqrt {2+\sqrt {3}} x}+c_4 e^{-2 \sqrt {2+\sqrt {3}} x} \]