71.10.5 problem 5

Internal problem ID [14500]
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 : 5
Date solved : Tuesday, January 28, 2025 at 06:42:41 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+8 y^{\prime \prime }-8 y^{\prime }+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 24

dsolve(diff(y(x),x$4)-4*diff(y(x),x$3)+8*diff(y(x),x$2)-8*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 30

DSolve[D[y[x],{x,4}]-4*D[y[x],{x,3}]+8*D[y[x],{x,2}]-8*D[y[x],x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x ((c_4 x+c_3) \cos (x)+(c_2 x+c_1) \sin (x)) \]