xydx + (x^2+y2)dy = 0 Prove that it is a Homogenous DE using homegeneity test (degree n)and solve for general solution, arbitrary constant and its particular solution.

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A: Given, f′(x)=8x​,​ f(4​)=47.

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A: Given data:- Total number of mangoes = 80 Bad mangoes = 8 Unripe mangoes = 22

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A: The answer is given below:

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A: I am attaching image so that you understand each and every step.

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A: As we know that; The Power law: ddxxn=nxn-1 The Product rule: f·g'=f'·g+f·g' The Chain rule:…