Answer:
30
Step-by-step explanation:
The characteristic solution follows from solving the characteristic equation,

so that

A guess for the particular solution may be

, but this is already contained within the characteristic solution. We require a set of linearly independent solutions, so we can look to

which has second derivative

Substituting into the ODE, you have



Therefore the particular solution is

Note that you could have made a more precise guess of

but, of course, any solution of the form

is already accounted for within

.
Answer:
f(x) + k
Explanation:
Vertical shift is represented by adding/subtracting a constant from the original given equation.
If the constant added is +ve, this means that the curve is vertically shifted upwards
If the constant added is -ve, this means that the curve is vertically shifted downwards.
Now, for the given, we have the original function f(x) and the constant k, therefore, to shift the graph vertically, the new function would be f(x)+k
We have:
f(x) = x² and k = -3
This means that the new function would be:
x² - 3
Since the constant is -ve, we can conclude that the curve is shifted vertically downwards by 3 units
Hope this helps :)