Question

Set up but do not solve for the appropriate particular solution yp for the differential equationy′′+9y=−3xsin(3x)using the Method of Undetermined Coefficients (primes indicate derivatives with respect to x).In your answer, give undetermined coefficients as A, B, etc.

Answer 1

Answer:

First find solution to homogeneous DE y" + 4y = 0:

Characteristic eqn => r^2 + 4 = 0 => r = +/- 2i

y_h = C_1*sin(2x) + C_2*cos(2x)

So our particular solution will be of the form yp = (Ax + B)*sin(2x) + (Cx + D)*cos(2x)

However since Bsin(2x) and Dcos(2x) are already solutions to the homogeneous DE, we multiply the yp through by x:

yp = (Ax^2 + Bx)*sin(2x) + (Cx^2 + Dx)*cos(2x)

Step-by-step explanation: