Internal problem ID [2214]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 23, page 106
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 n^{2} y^{\prime }+n^{4} y=\sin \left (k x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 61
dsolve(diff(y(x),x$2)+2*n^2*diff(y(x),x)+n^4*y(x)=sin(k*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (n^{4}+k^{2}\right )^{2} \left (c_{1} x +c_{2} \right ) {\mathrm e}^{-n^{2} x}+\left (n^{4}-k^{2}\right ) \sin \left (k x \right )-2 \cos \left (k x \right ) k \,n^{2}}{\left (n^{4}+k^{2}\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.198 (sec). Leaf size: 64
DSolve[y''[x]+2*n^2*y'[x]+n^4*y[x]==Sin[k*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\left (n^4-k^2\right ) \sin (k x)}{\left (k^2+n^4\right )^2}-\frac {2 k n^2 \cos (k x)}{\left (k^2+n^4\right )^2}+(c_2 x+c_1) e^{-n^2 x} \]