 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2017/paper-2/7/b/solution

y_{p} = A cos 4 x

. Substitution gives

(- 16 + 9) A cos 4 x = - 7 cos 4 x

, so

A = 1

. Hence

y_{p} = cos 4 x .

The forcing frequency differs from the homogeneous frequency, so no resonant factor of

x

is needed.

 New to topics? Read the docs here!