 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2008/paper-2/13/i/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

(r - 3) (r - 4) = 0

gives complementary terms

C e^{3 x} + D e^{4 x}

12 x + 7

, since its substitution gives

144 x

C + D = - 7

and

3 C + 4 D = - 12

, hence

y = 12 x + 7 - 16 e^{3 x} + 9 e^{4 x} .

 New to topics? Read the docs here!