73.8.19 problem 13.3 (d)

Internal problem ID [15227]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 13. Higher order equations: Extending first order concepts. Additional exercises page 259
Problem number : 13.3 (d)
Date solved : Tuesday, January 28, 2025 at 07:50:25 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }&=-2 y^{\prime \prime \prime } \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 28

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

\[ y(x)\to -\frac {1}{8} c_1 e^{-2 x}+x (c_4 x+c_3)+c_2 \]