You have,Originally Posted byfrozenflames

This, is a 'seperable differencial equation' .

Thus, express as,

Thus, integrating,

.

Thus,

Thus,

Thus,

Thus,

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Now, we have that

Thus,

Thus,

Meaning, the function is,

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The domain of

is what values can take. Notice the logarithm, which is only defined for positive real numbers. Thus,

Solving this inequality, and rationalizing the root

.

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The range for

is the values or such as, this equation is a solution for . Notice, that this equation has a solution for any thus, the range is all real numbers.