82.33.1 problem Ex. 1

Internal problem ID [18894]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. Examples on chapter VI, page 80
Problem number : Ex. 1
Date solved : Tuesday, January 28, 2025 at 12:33:50 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 33

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

\[ y \left (x \right ) = c_{1} {\mathrm e}^{x} \sin \left (x \right )+c_{2} {\mathrm e}^{x} \cos \left (x \right )+c_3 \,{\mathrm e}^{-x} \sin \left (x \right )+c_4 \,{\mathrm e}^{-x} \cos \left (x \right ) \]

✓ 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]
 

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