Question

1. Find a Trial Solution for the following DE: D (D2 -4D +13)2 2r +3r e cos (3r) 4e sin (3r)

Answer 1

Trial solution of the first part of RHS:

f(r) 21

This is a first degree polynomial,

Trial solution is:

g(x) = Ar + B

Trial solution of the second part of RHS:

This is a second degree polynomial with exponential and cosine term.

Trial solution is:

Trial solution of the third part of RHS:

f(x)42 sin (3r)

This is exponential and cosine term.

Trial solution is:

e cos(3x

The actual trial solution is sum of all three parts.

g(x) = Ar + B

e cos(3x