64.10.23 problem 23

Internal problem ID [13429]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 23
Date solved : Tuesday, January 28, 2025 at 05:42:17 AM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 61

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

\[ y = \left (-{\mathrm e}^{-\frac {\sqrt {2}\, x}{2}} c_{1} -{\mathrm e}^{\frac {\sqrt {2}\, x}{2}} c_{2} \right ) \sin \left (\frac {\sqrt {2}\, x}{2}\right )+\left (c_{3} {\mathrm e}^{-\frac {\sqrt {2}\, x}{2}}+{\mathrm e}^{\frac {\sqrt {2}\, x}{2}} c_4 \right ) \cos \left (\frac {\sqrt {2}\, x}{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 65

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

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