Consider the differential equation defined by the auxiliary equation (D² - 1)y = 0. Find the particular solution of the given differential equation if x 0 - 3; and y - 0.

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A: We have to answer given Questions.

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A: We can find differential equations.

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Q: 39 Find the sum of the series sin x + 3 sin 3x +5 sin 5x +...+(2k − 1) sin (2k-1)x

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A: The question is from stability analysis.

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Q: 1. If X is binomial random variable with E(X) = 2 and Var. X=4/3. Find P(X <4)

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A: Orthogonal complement of the space

Q: 44 If x = a[cost +-log tan² t dy T and y = a sint, then find at t= - dx 4

A: x=acost+12logtan2ty=asintt=π4