Internal problem ID [2740]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 4. Linear Differential Equations. Page 183
Problem number: 8.
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 }-4 y^{\prime \prime }+16 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 48
dsolve(diff(y(x),x$4)-4*diff(y(x),x$2)+16*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\sqrt {3}\, x} \sin \relax (x )-c_{2} {\mathrm e}^{-\sqrt {3}\, x} \sin \relax (x )+c_{3} {\mathrm e}^{\sqrt {3}\, x} \cos \relax (x )+c_{4} {\mathrm e}^{-\sqrt {3}\, x} \cos \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 49
DSolve[y''''[x]-4*y''[x]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-\sqrt {3} x} \left (c_2 \cos (x)+c_4 \sin (x)+e^{2 \sqrt {3} x} (c_3 \cos (x)+c_1 \sin (x))\right ) \\ \end{align*}