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1. Factorising denominator of fraction:x^2 + 10x + 21 = (x+3)(x+7)2) Partial fractions:f(x) = 12/(x+3)(x+7);  let f(x) = A/(x+3) + B/(x+7)then equating the nomi...

First find an auxiliary equation, for the complimentary function:m^2 + 2m - 3 = 0, (m+3)(m-1)=0m=1 or m=-3So the complimentary function is: x= Ae^t + Be^-3tFor the particular integral (PI), let x = Ue^-tt...

Firstly please show me what was the topic and the example in class. Given the topic I will provide the answer and the easiest way to complete it.
For example, let's say the student had to solve the ...

de Moivre's theorem gives us that (cos(x) + i sin(x))ⁿ = cos(nx) + i sin(nx), for integers n and real values x.Therefore cos(5x) + i sin(5x) = (cos(x) + i sin(x))⁵ = cos⁵(...

State de Moivre's theorem. Use n =5 and solve. I'll show this on the whiteboard.