Top answers

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=e mx . This gives y'=me mx and y''=m 2 e mx . Substituting into the differntial equation we get: m 2 e mx -12me mx -13e mx =0 Since e mx >0 divide throughout by e mx ...
AP
7060 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^-x)...
TR
3794 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 sides (rt(3+4i))^2=(a...
AA
3819 Views

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

Our given equation is d 2 x/dt 2 + 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 2 +5m +6= 0. ( Side note: ...
DM
6892 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 thi...
CB
38891 Views