15.11.20 problem 20

Internal problem ID [3130]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 19, page 86
Problem number : 20
Date solved : Monday, January 27, 2025 at 07:22:34 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 48

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

\[ y = \frac {\sin \left (k x \right )}{\left (k -n \right )^{2} \left (k +n \right )^{2}}+c_{1} \cos \left (n x \right )+c_2 \sin \left (n x \right )+c_3 \cos \left (n x \right ) x +c_4 \sin \left (n x \right ) x \]

✓ Solution by Mathematica

Time used: 0.530 (sec). Leaf size: 69

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

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