5.16 problem 28

Internal problem ID [4298]

Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section: Chapter 8, Ordinary differential equations. Section 5. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND ZERO RIGHT-HAND SIDE. page 414
Problem number: 28.
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: 0.001 (sec). Leaf size: 33

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

\[ y \relax (x ) = c_{1} \sin \relax (x ) {\mathrm e}^{-x}+c_{2} \cos \relax (x ) {\mathrm e}^{-x}+c_{3} {\mathrm e}^{x} \sin \relax (x )+c_{4} {\mathrm e}^{x} \cos \relax (x ) \]

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*}