Internal problem ID [2789]
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]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+17 y=\frac {64 \,{\mathrm e}^{-x}}{3+\sin \left (4 x \right )^{2}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 70
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)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-x} \left (4 \sin \left (4 x \right ) \sqrt {3}\, \arctan \left (\frac {\sqrt {3}\, \sin \left (4 x \right )}{3}\right )+3 \ln \left (\cos \left (4 x \right )+2\right ) \cos \left (4 x \right )-3 \ln \left (\cos \left (4 x \right )-2\right ) \cos \left (4 x \right )+3 \cos \left (4 x \right ) c_{1} +3 \sin \left (4 x \right ) c_{2} \right )}{3} \]
✓ Solution by Mathematica
Time used: 0.238 (sec). Leaf size: 72
DSolve[y''[x]+2*y'[x]+17*y[x]==64*Exp[-x]/(3+Sin[4*x]^2),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} e^{-x} \left (4 \sqrt {3} \sin (4 x) \arctan \left (\frac {\sin (4 x)}{\sqrt {3}}\right )+3 c_1 \sin (4 x)+3 \cos (4 x) (-\log (2-\cos (4 x))+\log (\cos (4 x)+2)+c_2)\right ) \]