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Lecture

# 9.1 Modelling with Differential Equations Question #2 (Medium)

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University of Toronto St. George

Mathematics

MAT136H1

all

Winter

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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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