Question

3. Solve each of the following constant coefficient ordinary differential equations: (10 pts] a) y"+ 3y'- 28y = 0

Answer 1

`y(t) = C_1e^(4t) + C_2e^(-7t)`

Explanation:

We are given the following information in the question:

`y''+3y'-28y = 0`

This can be written as:

`(D^2 + 3D - 28)y = 0`

The auxiliary equation obtained is:

`m^2+ 3m - 28 = 0\\ m^2 + 7m - 4m - 28 = 0\\m(m+7)-4(m+7)=0\\(m-4)(m+7)\\m = 4, m = -7`

Thus, the general solution of the equation is:

`y(t) = C_1e^(4t) + C_2e^(-7t)\\\text{where } C_1, C_2 \text{ are constants}`