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Further Mathematics

A Level

Solve the second order ODE, giving a general solution: x'' + 2x' - 3x = 2e^-t

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...

Answered by Isaac F. • Further Mathematics tutor

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I do not understand this topic and particularly this example. In the class the result was found out but I still do not get it. How did the teacher came up with this outcome?

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 ...

Answered by Madalin F. • Further Mathematics tutor

2004 Views

Use de Moivre's theorem to calculate an expression for sin(5x) in terms of sin(x) only.

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(...

Answered by Callum B. • Further Mathematics tutor

28986 Views

Use de Moivre’s theorem to show that, (sin(x))^5 = A sin(5x) + Bsin(3x) + Csin(x), where A , B and C are constants to be found.

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

Answered by Robbie M. • Further Mathematics tutor

5151 Views

Find all of the roots of unity, Zn, in the case that (Zn)^6=1

Here we use the complex exponential form of 1 which is e^(i 2n pi). Applying the sixth root and substituting in for integer values of n gives all roots in complex exponential form.These can be converted i...

Answered by Callum R. • Further Mathematics tutor

2244 Views