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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(x^3) Now integrate the entire equation and ...

In complex number ( especially for any real number) x and integer n it holds that (cos(x) + i(sinx))^n = cos(n x) + isin(n x) where i is the imaginary unit representing as i*i = -1. This is called De Moivre'...

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 of the derivative o...

Let P( n ) be the statement that 11 n - 6 is divisible by 5. BASE CASE : L et n = 1. This gives 11 1 - 6 = 5 , obviously divisible by 5, therefore we know that P(1) is true. HYPOTHOSIS STEP : Assume that P( ...

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 6-7i...