12.18.33 problem section 9.2, problem 43(g)

Internal problem ID [2147]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient. Page 483
Problem number : section 9.2, problem 43(g)
Date solved : Monday, January 27, 2025 at 05:42:49 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}+y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 53

dsolve(diff(y(x),x$5)+diff(y(x),x$4)+diff(y(x),x$3)+diff(y(x),x$2)+diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

\[ y = \left (\left (c_3 \,{\mathrm e}^{\frac {x}{2}}+{\mathrm e}^{\frac {3 x}{2}} c_5 \right ) \cos \left (\frac {\sqrt {3}\, x}{2}\right )+\left ({\mathrm e}^{\frac {3 x}{2}} c_4 +c_2 \,{\mathrm e}^{\frac {x}{2}}\right ) \sin \left (\frac {\sqrt {3}\, x}{2}\right )+c_1 \right ) {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 70

DSolve[D[y[x],{x,5}]+D[y[x],{x,4}]+D[y[x],{x,3}]+D[y[x],{x,2}]+D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (e^{x/2} \left (c_3 e^x+c_2\right ) \cos \left (\frac {\sqrt {3} x}{2}\right )+e^{x/2} \left (c_4 e^x+c_1\right ) \sin \left (\frac {\sqrt {3} x}{2}\right )+c_5\right ) \]