82.33.10 problem Ex. 10

Internal problem ID [18903]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. Examples on chapter VI, page 80
Problem number : Ex. 10
Date solved : Tuesday, January 28, 2025 at 12:34:03 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y&=\cos \left (m x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.224 (sec). Leaf size: 48

dsolve(diff(y(x),x$4)+2*n^2*diff(y(x),x$2)+n^4*y(x)=cos(m*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\cos \left (m x \right )}{\left (m -n \right )^{2} \left (m +n \right )^{2}}+c_{1} \cos \left (n x \right )+c_{2} \sin \left (n x \right )+c_3 \cos \left (n x \right ) x +c_4 \sin \left (n x \right ) x \]

✓ Solution by Mathematica

Time used: 0.461 (sec). Leaf size: 60

DSolve[D[y[x],{x,4}]+2*n^2*D[y[x],{x,2}]+n^4*y[x]==Cos[m*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\cos (m x)+\left (m^2-n^2\right )^2 ((c_2 x+c_1) \cos (n x)+(c_4 x+c_3) \sin (n x))}{(m-n)^2 (m+n)^2} \]