Internal problem ID [2240]
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 8.3, The Method of Undetermined
Coefficients. page 525
Problem number: Problem 29.
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 }+5 y-3 \sin \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 37
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+5*y(x)=3*sin(2*x),y(x), singsol=all)
\[ y \relax (x ) = \sin \left (2 x \right ) {\mathrm e}^{-x} c_{2}+\cos \left (2 x \right ) {\mathrm e}^{-x} c_{1}+\frac {3 \sin \left (2 x \right )}{17}-\frac {12 \cos \left (2 x \right )}{17} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 44
DSolve[y''[x]+2*y'[x]+5*y[x]==3*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {3}{17} (4 \cos (2 x)-\sin (2 x))+e^{-x} (c_2 \cos (2 x)+c_1 \sin (2 x)) \\ \end{align*}