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To begin with, we should find the equation of the line. To do this we appoint a position vector and a direction vector. The position vector can simply be one of the two points we are give, i.e. (6,4,1). T...

Induction is a method that can be used to prove that a mathematical statement holds for possitive integers, n. It usually consists of four steps, as follows:  1) Basis: Show that the statement to be prove...

divide through by 2x to get: dy/dx + 2y/x = 4x         this is now in the form of dy/dx + P(x)y = Q(x)

intergrating factor = exp( integral(P(x)) dx ) = exp( integr...

Write y = sinh^(-1)(x) ie x = sinhy. Then writing this in terms of exponentials and multiplying by 2 we will get 2x = exp(y) - exp(-y). Multiply by exp(y) and rearrange to obtain exp(2y) - 2xexp(y) -1 = 0...

This is a first order differential equation, but initially it is not solvable as both the X&Y's can't be separated from eachother directly. An integrating factor is a specific value that when multipli...