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A: Follow the procedure given below. 

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Q: Find (with proof) all the triplets of integers a, b, c that satisfy a? + b² = 6c².

A: Note: (a,b,c) = (0,0,0) is the trivial solution. We will look for non-trivial solutions.  

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A: We will use the following formula to find the second derivative i.e d/dx(xn)=nxn-1

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A: Given:      2x13- 4x16 - 6=0

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A: Rate of Phase transformation is gievn bydydt=4kt3(1-y)We need to find y as function of t.  

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Q: Determine the general solution of the given differential equations): | (A – 2xy) dx + 3x²dy = 0 a.

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