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Q: 1. Solve using the Laplace transform: y" - 3y' = sin(2t), y(0) = 1, y'(0) = 2.

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Q: Is the following statement necessarily true? Provide a proof or a counterexample. If h : A → B, g :…

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Q: In a test of a sex-selection technique, results consisted of 242 female babies and 15 male babies.…

A: Number of female babies =242 Number of male babies = 15 Total babies = 242+15…

Q: e: у"+у%3 (t - 2) и(t - 2),

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Q: Consider the function h : N → N given by h(n) = n + (-1)*+l.

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Q: regional automobile dealership sent out fliers to prospective customers indicating that they had…

A: From the part b and c we get.

Q: 2. Solve the differential equation x- 2y = r° cos() on (0, 00). %3D COS

A: To solve the given differential equation.

Q: 1) y'+ = 5, y(1) = 4 Solve

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Q: Form the differential equations from the following 1. y= ax + bx², 3. xy Ae +Be +x. %3D

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Q: 2) Solve ² y' = y(0) = 1 %3D 2 y+ 1 '

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Q: Solve (1- x2)y" +2xy'-2y = 0 on (-1,1) given that y1 = x is a solution.

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Q: Q1. 52% percent of the students at a certain college are females. 5% of the students in this college…

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A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…