d?y Consider the second-order differential equation dt? + 49y = 2 sin(8t). Find the Particular Integral (response to forcing) and enter it here: y,

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A: First we rewrite the series and then find the sum.

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A: A detailed solution is given below.

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A: Taylor series of function fx at a is defined as:…

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A: Let's calculate radius of convergence and interval of convergence of the given series.

Q: 18-19. In xy = 4, let x and y be differentiable functions of t. Evaluate at x = 10 and = 20. dt dy…

A: A detailed solution is given below.

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A: Given, f(x)=3x+1 To be found : f"'(3)

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A: Here I am providing my handwritten solution

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A: We have to find f'(x) and f'(1).

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A: We can explain the answer as below.

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A: Find the dy/dx

Q: evaluate

A: We will solve the integration

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A: In order to find all the asked intervals or points appropriate conditions need to be applied.

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A: We will solve this system of equations algebraically.

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A: Please refer to the image below

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A: given

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A: Given

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A: Follow the procedure given below.

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A: As per guidelines we can answer only one question at a time, so if you need more answer kindly…

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