Internal problem ID [2738]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 4. Linear Differential Equations. Page 183
Problem number: 6.
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=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 33
dsolve(diff(y(x),x$4)+4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-x} \sin \relax (x )+c_{2} {\mathrm e}^{-x} \cos \relax (x )+c_{3} {\mathrm e}^{x} \sin \relax (x )+c_{4} {\mathrm e}^{x} \cos \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 38
DSolve[y''''[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} (c_1 \cos (x)+c_2 \sin (x))+e^x (c_4 \cos (x)+c_3 \sin (x)) \\ \end{align*}