35.5.16 problem 28

Internal problem ID [6150]
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
Date solved : Monday, January 27, 2025 at 01:38:28 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+4 y&=0 \end{align*}

✓ 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)
 

\[ y = c_1 \,{\mathrm e}^{x} \sin \left (x \right )+c_2 \,{\mathrm e}^{x} \cos \left (x \right )+c_3 \,{\mathrm e}^{-x} \sin \left (x \right )+c_4 \,{\mathrm e}^{-x} \cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 40

DSolve[D[y[x],{x,4}]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (\left (c_4 e^{2 x}+c_1\right ) \cos (x)+\left (c_3 e^{2 x}+c_2\right ) \sin (x)\right ) \]