Question

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

Answer 1

Answer:

$y(t) = C_1e^{4t} + C_2e^{-7t}$

Step-by-step 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:

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