Internal problem ID [2280]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.7, The Variation of Parameters
Method. page 556
Problem number: Problem 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }+17 y-\frac {64 \,{\mathrm e}^{-x}}{3+\sin ^{2}\left (4 x \right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 73
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+17*y(x)=64*exp(-x)/(3+sin(4*x)^2),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x} \sin \left (4 x \right ) c_{2}+{\mathrm e}^{-x} \cos \left (4 x \right ) c_{1}+\frac {4 \left (\sin \left (4 x \right ) \sqrt {3}\, \arctan \left (\frac {\sqrt {3}\, \sin \left (4 x \right )}{3}\right )-\frac {3 \cos \left (4 x \right ) \left (\ln \left (\cos \left (4 x \right )-2\right )-\ln \left (\cos \left (4 x \right )+2\right )\right )}{4}\right ) {\mathrm e}^{-x}}{3} \]
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 61
DSolve[y''[x]+2*y'[x]+17*y[x]==64*Exp[-x]/(3+Sin[4*x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} e^{-x} \left (3 \cos (4 x) \left (2 \coth ^{-1}(2 \sec (4 x))+c_2\right )+\sin (4 x) \left (4 \sqrt {3} \cot ^{-1}\left (\sqrt {3} \csc (4 x)\right )+3 c_1\right )\right ) \\ \end{align*}