71.10.6 problem 6

Internal problem ID [14501]
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 : 6
Date solved : Tuesday, January 28, 2025 at 06:42:42 AM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 36

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

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

✓ Solution by Mathematica

Time used: 0.238 (sec). Leaf size: 56

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

\[ y(x)\to \int _1^xe^{-K[1]} \left (e^{3 K[1]} c_1+c_2 \cos \left (\sqrt {3} K[1]\right )+c_3 \sin \left (\sqrt {3} K[1]\right )\right )dK[1]+c_4 \]