Prove that the following differential equation: (1 + x2)y'' + 2xy' - 2y = 0 has the following expression as a solution: y = c0 (1 + xTan-1x) + c1x

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A: Explanation of the answer is as follows

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A: you should write a bracket

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A: Ye

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Q: 2x +3 x:²-9 da

A: To evaluate the given integral.

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Q: Find the inverse Laplace transform L-¹{F(s)} of the given function. 12 s² + 16 Your answer should be…

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Q: Show that for integers a, n satisfying 0 < a <n, ged(a, n) = gcd(n, n-a)

A: Solution is given below: