Each of the following differential equations has an integrating factor depending on only one variable. Find the integrating factor and solve the equation. (a) (4y-x2) dx + x dy = 0 (b) (2xy2-y) dx + (2x-x²y) dy = 0 (c) 2 dx + (2x-3y-3) dy = 0; y(2) (d) (2y sin x + 3y4 sin x cos x) dx - (4y³ cos²x+cos x) dy = 0

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A: Please see the below picture for detailed solution.

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A: Please see the below picture for detailed solution.

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A: We can solve it by Lagrange Interpolation Formula given below

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A: Here are the solution:

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A: We have to find v and a.

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A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

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A: We can find the answer as below.

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A: Here is the solution:

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A: solution is given below

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A: The given points are:   x1, y1,  x2, y2  and  x3, y3

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A: Derivative

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A: Need to find out the integration.

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A: As per the instruction, we will be answering the first one.

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A: A detailed solution is given below.

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A: ,

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