Internal problem ID [290]
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.
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 }-16 y^{\prime \prime }+16 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 75
dsolve(diff(y(x),x$4)-16*diff(y(x),x$2)+16*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\left (-\sqrt {3}\, \sqrt {2}-\sqrt {2}\right ) x}+c_{2} {\mathrm e}^{\left (\sqrt {3}\, \sqrt {2}+\sqrt {2}\right ) x}+c_{3} {\mathrm e}^{\left (-\sqrt {3}\, \sqrt {2}+\sqrt {2}\right ) x}+c_{4} {\mathrm e}^{\left (\sqrt {3}\, \sqrt {2}-\sqrt {2}\right ) x} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 70
DSolve[y''''[x]-16*y''[x]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 \sqrt {2+\sqrt {3}} x} \left (c_1 e^{2 \sqrt {6} x}+c_2 e^{2 \sqrt {2} x}+c_3 e^{4 \sqrt {2+\sqrt {3}} x}+c_4\right ) \\ \end{align*}