Internal problem ID [2160]
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: 21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 n y^{\prime }+n^{2} y=5 \cos \left (6 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 53
dsolve(diff(y(x),x$2)+2*n*diff(y(x),x)+n^2*y(x)=5*cos(6*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (n^{2}+36\right )^{2} \left (c_{1} x +c_{2} \right ) {\mathrm e}^{-n x}+5 \cos \left (6 x \right ) n^{2}+60 \sin \left (6 x \right ) n -180 \cos \left (6 x \right )}{\left (n^{2}+36\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 57
DSolve[y''[x]+2*n*y''[x]+n^2*y[x]==5*Cos[6*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {5 \cos (6 x)}{n^2-72 n-36}+c_1 e^{\frac {n x}{\sqrt {-2 n-1}}}+c_2 e^{-\frac {n x}{\sqrt {-2 n-1}}} \]