11.2.9 problem 16

Internal problem ID [1480]
Book : Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima, Meade
Section : Chapter 4.2, Higher order linear differential equations. Constant coefficients. page 180
Problem number : 16
Date solved : Monday, January 27, 2025 at 04:57:48 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 26

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

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