73.12.25 problem 19.4 (i)

Internal problem ID [15377]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 19. Arbitrary Homogeneous linear equations with constant coefficients. Additional exercises page 369
Problem number : 19.4 (i)
Date solved : Tuesday, January 28, 2025 at 07:53:53 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+16 y^{\prime }-16 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 26

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 32

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

\[ y(x)\to e^{-2 x} \left (e^{4 x} (x (c_4 x+c_3)+c_2)+c_1\right ) \]