Internal problem ID [1494]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient.
Page 483
Problem number: section 9.2, problem 43(c).
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 }+64 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 45
dsolve(diff(y(x),x$4)+64*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-2 x} \sin \left (2 x \right )+c_{2} {\mathrm e}^{-2 x} \cos \left (2 x \right )+c_{3} {\mathrm e}^{2 x} \sin \left (2 x \right )+c_{4} {\mathrm e}^{2 x} \cos \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 44
DSolve[y''''[x]+64*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x} \left (\left (c_4 e^{4 x}+c_1\right ) \cos (2 x)+\left (c_3 e^{4 x}+c_2\right ) \sin (2 x)\right ) \\ \end{align*}