40.8.10 problem 25

Internal problem ID [6710]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 13. Homogeneous Linear equations with constant coefficients. Supplemetary problems. Page 86
Problem number : 25
Date solved : Monday, January 27, 2025 at 02:24:35 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (6\right )}+9 y^{\prime \prime \prime \prime }+24 y^{\prime \prime }+16 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 33

dsolve(diff(y(x),x$6)+9*diff(y(x),x$4)+24*diff(y(x),x$2)+16*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_6 x +c_4 \right ) \cos \left (2 x \right )+\left (c_5 x +c_3 \right ) \sin \left (2 x \right )+\sin \left (x \right ) c_1 +\cos \left (x \right ) c_2 \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 40

DSolve[D[y[x],{x,6}]+9*D[y[x],{x,4}]+24*D[y[x],{x,2}]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (c_2 x+c_1) \cos (2 x)+c_6 \sin (x)+\cos (x) (2 (c_4 x+c_3) \sin (x)+c_5) \]