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It looks like you're asked to find the value of y(-1) given its implicit derivative,
and with initial condition y(2) = -1.
The differential equation is separable:
Integrate both sides:
Solve for y :
Use the initial condition to solve for C :
Then the particular solution to the differential equation is
and so
From your equation, you can see that you have a difference of two cubes (aka two cubes being subtracted): 64, which is 
, and 
.
There is rule for the difference of two cubes:
The difference of two cubes is equal to the difference of the cube roots times a binomial, which is the sum of the squares of the roots plus the product of the roots.
That sounds pretty confusing, but it's much easier to understand when put mathematically. Let's say our two cubes are
and 
. The difference of those two cubes is:
In our problem, a = 4 (since = 64) and b = y (since 
. Plug these values into the rule to find the factor of 
:
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Answer:
There is rule for the difference of two cubes:
The difference of two cubes is equal to the difference of the cube roots times a binomial, which is the sum of the squares of the roots plus the product of the roots.
That sounds pretty confusing, but it's much easier to understand when put mathematically. Let's say our two cubes are
In our problem, a = 4 (since
-----
Answer:
