Inhomogeneous diff. eq.

1. Oct 4, 2007

kasse

y''+4y = x*sin2x

Find a particular solution using the method of undetermined coefficients.
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No idea what to do here. My table has no suggestion for a particular solution when r(x) = x*sin2x.

2. Oct 4, 2007

rock.freak667

The RHS consists of the product of a Polynomial of degree one and a trig function

so the P.I. would be (P.I.of the polynomial)*(P.I. for the trig function)

3. Oct 5, 2007

HallsofIvy

Staff Emeritus
You don't learn mathematics by using tables, you learn mathematics by using concepts. For sin(2x) on the right hand side your first thought should be Acos(2x)+ Bsin(2x). With "x" you would try Ax+ B. As rockfreak667 said, combine those ideas:
try y= (Ax+B)sin(2x)+ (Cx+ D)cos(2x)

HOWEVER, sin(2x) and cos(2x) already satisfy the differential equation! I'm sure you already know what to do in that situation- multiply by x. Try (Ax2+ Bx)sin(2x)+ (Cx2+ Dx)cos(2x).

I suspect that, since the equation only involves "even" derivatives, you don't need all of those coefficients- some will be 0- but I see no good way to figure out which in advance.