Internal problem ID [2764]
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 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+y=50 \sin \left (3 x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=50*sin(3*x),y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{1} x +c_{2} \right ) {\mathrm e}^{-x}-3 \cos \left (3 x \right )-4 \sin \left (3 x \right ) \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 34
DSolve[y''[x]+2*y'[x]+y[x]==50*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -3 \cos (3 x)+e^{-x} \left (-4 e^x \sin (3 x)+c_2 x+c_1\right ) \]