Solve the given initial-value problem. The DE is a Bernoulli equation. y1/2 dy +y dx y3/2 = 1, y(0) = 9 In(x-1)=²x-In (26) + ln 2 X

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A: Please check step 2 for solution.!

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A: Given , (a).   ∫15∫2y2 6x2y dx dy  = ∫  dy (b).    ∫15∫2x26x2y dydx =∫ dx now we solve the given…

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A: Kindly refer to Step 2 for the solution.

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Q: Suppose an >0 and an diverges. Prove that n=1 n=1 an an +1 diverges.

A: Given that an>0, and ∑n=1∞an diverges. To prove that ∑n=1∞anan+1 diverges.