Let x be the particular solution

for and .

Step-by-step explanation:

The given differential equation is

Rearranging it as

where C is constant.

The initial condition is f(-1)=-1, i.e for x=-1, y=-1.

So, by using the initial condition to get the value of constant:

From equation (i), we have

As y=f(x), so the required particular solution

Now, determining the domain of the function

As for a real value output, the term under square root must be positive.

So,

Therefore, the domain of the function is

Hence, for and .

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents

answer: translate the circles so they share a common center point and dilate circle y by a scale factor of 3.