11.2.6 problem 13

Internal problem ID [1477]
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 : 13
Date solved : Monday, January 27, 2025 at 04:57:47 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (6\right )}-y^{\prime \prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 27

dsolve(diff(y(x),x$6)-diff(y(x),x$2)=0,y(x), singsol=all)
 

\[ y = c_1 +c_2 x +c_3 \,{\mathrm e}^{x}+c_4 \,{\mathrm e}^{-x}+c_5 \sin \left (x \right )+c_6 \cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.097 (sec). Leaf size: 38

DSolve[D[y[x],{x,6}]-D[y[x],{x,2}]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^x+c_3 e^{-x}+c_6 x-c_2 \cos (x)-c_4 \sin (x)+c_5 \]