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9.1 Modelling with Differential Equations Question #2 (Medium)

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9.1 Differential Equations Modeling With Differential Equations Question #2 (Medium): Forming Functions to Satisfy Differential Equation Strategy Given the differential equation, take the first and second derivative if necessary then equate to the differential equation to get missing parameters. Then with those determined values, plug into the family of the function given, simplify and show that it equals to the other side. Sample Question 1) For what values of does the function satisfy the differential equation ? 2) If and are values of found in part 1) show that every member of the family of function is also a solution. Solution 1) If the given function is to be a solution to the differential equation, then its first and second derivative must be taken first in order to plug into the differential equation to solve backwards for the missing parameter a. So the first derivative is:
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