Internal problem ID [2766]
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]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+4 y=169 \sin \left (3 x \right )} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{-2 x}+{\mathrm e}^{-2 x} x c_{1} -12 \cos \left (3 x \right )-5 \sin \left (3 x \right ) \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 36
DSolve[y''[x]+4*y'[x]+4*y[x]==169*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -12 \cos (3 x)+e^{-2 x} \left (-5 e^{2 x} \sin (3 x)+c_2 x+c_1\right ) \]