73.17.8 problem 8

Internal problem ID [15542]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 08:01:39 AM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 35

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

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