73.9.33 problem 14.5 (c)

Internal problem ID [15294]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 14. Higher order equations and the reduction of order method. Additional exercises page 277
Problem number : 14.5 (c)
Date solved : Tuesday, January 28, 2025 at 07:51:40 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+24 y^{\prime \prime }-32 y^{\prime }+16 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

dsolve(diff(y(x),x$4)-8*diff(y(x),x$3)+24*diff(y(x),x$2)-32*diff(y(x),x)+16*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 28

DSolve[D[y[x],{x,4}]-8*D[y[x],{x,3}]+24*D[y[x],{x,2}]-32*D[y[x],x]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} (x (x (c_4 x+c_3)+c_2)+c_1) \]