(a) Supposed that w = r'y- with a= est and y = rs sint. Find the value of when r = 0, s = 1,t=r. Assuming that the following equations define z an implicit function of z, y and, z = f(1,y), find for y3 +e(1-3) – sin(n2) = yz2 at (-1, },1). (b)

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A: We can solve this ordinary differential equation by undetermined coefficient

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A: Here, to match the graph of the given differential equation: y'=sin(10x)sin(10y)

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A: solution

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A: We will differentiate the  y twice to get desired differential equation

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A: Third order non homogeneous differential equation.

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A: We have to find the following derivatives

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Q: 4. (a) The velocity v and time t are related by the first order differential equation below. Find…

A: We will solve the problem.

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A: We can solve it using differential equation as below.

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A: Take Laplace transform of the differential equation and get Laplace transform of yt:…

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A: Since you have asked multiple questions in a single request. so we will answer only the first…

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