Question

Find the complementary solution, y c​ (t), with constants denoted c 1 ,c 2.

A) c 1 e 2t +c 2 e −3t
B) c 1 e −t +c 2 e 4t
C) c 1 e 3t +c 2 e −2t
D) c 1 e −2t +c 2 e t

Answer 1

The complementary solution is given by option D) c1e^(-2t) + c2e^t.

Step-by-step explanation:

The complementary solution, or the homogeneous solution, is the solution to the differential equation when the right-hand side of the equation is zero. To find the complementary solution, you need to solve the associated homogeneous equation. In this case, the complementary solution is given by option D) c1e^(-2t) + c2e^t.