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First Order Differential Equations and Values of Parameters

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1. Given satisfying , ; π ; find

2. Given such that , ; list all possible solutions. For which of these does ?; ?

3. Suppose for it is known that

Where "a" is a parameter. Determine the value of this parameter which ensure the existence of a relation such that , C a constant, for all satisfying (1) and then deduce . What is C if .

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First Order Differential Equations and Values of Parameters are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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1. Given satisfying , ; π ; find
This is linear equation. When compared to the general form of the linear equation , where P and Q are functions of x, we have . The solution for such equations is given by where C is arbitrary constant.
Plugging the values of P and Q in the above equation, we get the solution as
Hence the solution is given by . Given that π ; Plugging the value x=π in the above solution, we see that
. So the solution for the given equation is
2. Given ...

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