Some really basic maths help

Yeah, you can't simplify it any further than you have done already.

What's the rest of the question? Might be another way of doing it, I haven't used the whole -b+-/4ac thing for years.
 
If your auxiliary equation has complex roots, then it's pretty much the same except you should use Euler's formula to express the exponential in terms of cosine and sine. i.e. for complex numbers a+bi and a-bi:

e^(a+bi)x = (e^(ax)) * (cos(bx) + i*sin(bx))

e^(a-bi)x = (e^(ax)) * (cos(bx) - i*sin(bx))
 
Basically I need to solve the quadratic m+m+4=0

Which unless I am mistaken leaves me with the roots as


(-1+√-15)/2 and (-1-√-15)/2

which i've then made

(-1+√15i)/2 and (-1-√15i)/2

However I then need to use those for the rest of my problem (solving a differential equation) so having them like that is a slight pain :/

So long as that i is not under the square root, you're all good. Personally, I'd be writing it as i√15, just to be clear about it.
 
What is the next part of the question?

a) Find the Complementary Function
b) Determine a Particular Integral
c) Find the complete solution
d) Plot the curve of the solution x(t)

This quadratic stuff was part of a)

It's an inhomogeneous second order differential equation problem.

I'm not going to put the full problem up because it's coursework and I don't want to get kicked out of uni because they think I got you lot to do all my coursework for me :p
 
At last my 3rd year of maths at uni lets me do something useful. Judging by the type of problem your doing, and the fact that root15 can't be simplified to a more useful form, I'd guess you either have it in the appropriate form, or have made a prior mistake.
 
a) Find the Complementary Function
b) Determine a Particular Integral
c) Find the complete solution
d) Plot the curve of the solution x(t)

This quadratic stuff was part of a)

It's an inhomogeneous second order differential equation problem.

I'm not going to put the full problem up because it's coursework and I don't want to get kicked out of uni because they think I got you lot to do all my coursework for me :p

Oh well, good thing I guess, cos I hated that stuff, soooo booooring and tedious. :o :p More of an analysis man myself. :D :o
 
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