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What is the antiderivative of each of the following differential equations? Use implicit integration when necessary. Solve your equations for . Be careful about introducing the constant of integration at the appropriate time.

  1. Notice that the derivative is in terms of . Antidifferentiate!

  1. Compare and contrast part (a) with part (b).
    Which one requires implicit integration?

  1. Translation: The derivative is equal the the original function squared times a constant.
    What can you conclude about the original function?
    Is it linear, quadratic, cubic, exponential, trigonometric, etc.?
    Use implicit integration to check your conjecture.

  1. Translation: The derivative of this function is a constant.
    What can you conclude about the function?

  1. Explain the significance of the absolute value.