Answer:

Step-by-step explanation:
we want to figure out the general term of the following recurrence relation

we are given a linear homogeneous recurrence relation which degree is 2. In order to find the general term ,we need to make it a characteristic equation i.e
the steps for solving a linear homogeneous recurrence relation are as follows:
- Create the characteristic equation by moving every term to the left-hand side, set equal to zero.
- Solve the polynomial by factoring or the quadratic formula.
- Determine the form for each solution: distinct roots, repeated roots, or complex roots.
- Use initial conditions to find coefficients using systems of equations or matrices.
Step-1:Create the characteristic equation

Step-2:Solve the polynomial by factoring
factor the quadratic:

solve for x:

Step-3:Determine the form for each solution
since we've two distinct roots,we'd utilize the following formula:

so substitute the roots we got:

Step-4:Use initial conditions to find coefficients using systems of equations
create the system of equation:

solve the system of equation which yields:

finally substitute:


and we're done!
To find the maximum height, we must find the x value at which the maximum height occurs.
The maximum height occurs at x = 0 because that is where y is the largest.
When we plug x= 0 into the function that is given in the question, we get 630 ft.
Hope it helps!
The term "autonomous" refers to an ordinary differential equation that relates the derivatives of the dependent variable as a function *only* of the dependent variable. In other words, the ODE doesn't explicitly depend on the independent variable.
Examples:

is autonomous

is *not* autonomous