71.10.8 problem 8

Internal problem ID [14503]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.3, page 210
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 06:42:42 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 24

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

\[ y = c_{1} +{\mathrm e}^{2 x} c_{2} +c_{3} {\mathrm e}^{x}+c_4 \sin \left (x \right )+c_5 \cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 43

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

\[ y(x)\to \int _1^x\left (e^{K[1]} \left (c_3+e^{K[1]} c_4\right )+c_1 \cos (K[1])+c_2 \sin (K[1])\right )dK[1]+c_5 \]