Internal problem ID [2238]
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 27.
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-8 \sin \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)+4*y(x)=8*sin(2*x),y(x), singsol=all)
\[ y \relax (x ) = \sin \left (2 x \right ) c_{2}+\cos \left (2 x \right ) c_{1}-2 x \cos \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 29
DSolve[y''[x]+4*y[x]==8*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sin (x) \cos (x)+(-2 x+c_1) \cos (2 x)+c_2 \sin (2 x) \\ \end{align*}