AP Calculus AB : Solving separable differential equations and using them in modeling

Study concepts, example questions & explanations for AP Calculus AB

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Example Questions

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Example Question #21 : Applications Of Antidifferentiation

Solve the separable differential equation:

given the condition at

Possible Answers:

Correct answer:

Explanation:

To solve the separable differential equation, we must separate x and y to the same sides as their respective derivatives:

Next, we integrate both sides:

The integrals were solved using the identical rules.

The two constants of integration are now combined to make a single one:

Now, exponentiate both sides of the equation to solve for y, and use the properties of exponents to rearrange C:

Finally, we solve for the integration constant using the given condition:

Our final answer is

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