Answer: Hello!
A second order differential equation has the next shape:
where p(t), q(t) and g(t) are functions of t, that can be constant numbers for example.
And is called homogeneus when g(t) = 0, so you have:
Then a second order differential equation is homogeneus ef every term involve either y or the derivatives of y.
Answer:
I assume that the function is:
Now let's describe the general transformations that we need to use in this problem.
Reflection across the x-axis:
For a general function f(x), a reflection across the x-axis is written as:
g(x) = -f(x)
Reflection across the y-axis:
For a general function f(x), a reflection across the y-axis is written as:
g(x) = f(-x)
Then a reflection across the y-axis, and then a reflection across the x-axis is just:
g(x) = -(f(-x)) = -f(-x)
In this case, we have:
then:
Now we can graph this, to get the graph you can see below:
