Internal problem ID [2257]
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 8.4, Complex-Valued Trial
Solutions. page 529
Problem number: Problem 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y^{\prime }+4 y-169 \sin \left (3 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)+4*diff(y(x),x)+4*y(x)=169*sin(3*x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{-2 x}+{\mathrm e}^{-2 x} x c_{1}-5 \sin \left (3 x \right )-12 \cos \left (3 x \right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 31
DSolve[y''[x]+4*y'[x]+4*y[x]==169*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -5 \sin (3 x)-12 \cos (3 x)+e^{-2 x} (c_2 x+c_1) \\ \end{align*}