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Further Mathematics
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a) Find the general solution to the differential equation: f(x)=y''-12y'-13y=8. b) Given that when x=0, y=0 and y'=1, find the particular solution to f(x).

First consider y''-12y'-13y=0.

Try: y=emx. This gives y'=memx and y''=m2emx.

Substituting into the differntial equation we get: m2e

AP
6532 Views

How do I prove that the differential of coshx is equal to sinhx?

Before this proof, it is important to appreciate that both of these hyperbolic  functions can be written in terms of e^x. Therefore, before you begin to differentiate, you must represent coshx as (e^x + e...

TR
3309 Views

Find the root of the complex 3+4i

What we should know is that the root 3+4i is a complex number that looks alot like a+bi.

We can say : rt(3+4i) = a+bi (Where we dont know what a & b is..yet)

and when we square both side...

AA
3419 Views

How would I solve the following equation d^2x/dt^2 + 5dx/dt + 6x = 0

Our given equation is d2x/dt2 + 5dx/dt + 6x = 0, which we need to recognise as a second order differential equation. Therefore we need to begin by solving the auxilary funtion m...

DM
6325 Views

Why is the integral of 1/sqrt(1-x^2)dx = sin^{-1}(x)?

This is an example of an integral that uses trigonometric substitutions, which is quite a common theme for A-level further maths questions. Firstly, notice the denominator is quite unpleasant, so to make ...

CB
34744 Views

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