Answer:
(See attached graph)
Step-by-step explanation:
To solve a second-order homogeneous differential equation, we need to substitute each term with the auxiliary equation where the values of
are the roots:
Since the values of are equal real roots, then the general solution is
.
Thus, the general solution for our given differential equation is .
To account for both initial conditions, take the derivative of , thus,
Now, we can create our system of equations given our initial conditions:
We then solve the system of equations, which becomes easy since we already know that :
Thus, our final solution is:
