12.18.8 problem section 9.2, problem 8

Internal problem ID [2122]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient. Page 483
Problem number : section 9.2, problem 8
Date solved : Monday, January 27, 2025 at 05:42:38 AM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

dsolve(diff(y(x),x$4)+diff(y(x),x$2)=0,y(x), singsol=all)
 

\[ y = c_1 +c_2 x +c_3 \sin \left (x \right )+c_4 \cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 24

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

\[ y(x)\to c_4 x-c_1 \cos (x)-c_2 \sin (x)+c_3 \]