Internal problem ID [2159]
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.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }+2 n^{2} y^{\prime \prime }+n^{4} y=\sin \left (k x \right )} \]
✓ Solution by Maple
Time used: 0.016 (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: 0.457 (sec). Leaf size: 69
DSolve[y''''[x]+2*n^2*y''[x]+n^4*y[x]==Sin[k*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {(c_2 x+c_1) \left (k^2-n^2\right )^2 \cos (n x)+(c_4 x+c_3) \left (k^2-n^2\right )^2 \sin (n x)+\sin (k x)}{(k-n)^2 (k+n)^2} \]