Search over 10,000 free study notes

Divide through by x so:      (dy/dx) +2(y/x) = 4x

Now multiply through by the intergrating factor:  e^(| (2/x) dx) = e^(2.ln(x)) = x^2

so you get:     (x^2)(dy/dx) + 2xy = 4...

In complex number ( especially for any real number) x and integer n it holds that

(cos(x) + i(sinx))^n = cos(nx) + isin(nx) where i is the imaginary unit repres...

At first glance, this may look like an inverse trig integral but as the top contains an x term, we must use a different method.

First, rewrite the top in two parts, one that is a multiple...

Let P(n) be the statement that 11ⁿ - 6 is divisible by 5.

BASE CASE: Let n = 1.  This gives 11¹ - 6 = 5, ...

The complex conjugate of a complex number is a number for which the real part is the same and for which the imaginary part has the same magnitude but opposite sign. e.g. the complex conjugate of 6+7i is 6...