Find the differential equation by eliminating the arbitrary constant/s. 1. y¹= x(2e + c) 2. y = Ae³x cos x+Be³* sin x 3. Obtain the DE of the family of circles with center at (2,-3). Draw at least 4 representative members of the family.

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A: We can solve the integration as below.

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A: Given problem:-

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A: Follow the procedure given below.

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A: Topic = Integrate

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A: We can find the answer as below.

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A: Here, we know that the power series of 11-x is: 11-x=∑n=0∞xn...(1)

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A: NOTE: Refresh your page if you can't see any equations. . the given equation is  take derivative

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A: Let's solve given integral.

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A: Solution

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A: Basic differentiation is required.

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A: Topic = Integration

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A: As per the rules we can answer only the first question and rest can be reposted.