d^2x/dt^2 - dx/dt - 12x = 0, where x = 12 and dx/dt = 13 when t = 0
Could I have a full explaination to this question?
Strong user name to slightly trollish question.
I'll try to translate what I think is going on anyway...
You're given...
$\displaystyle \frac{d^2x}{dt^2} - \frac{dx}{dt} - 12x = 0$.
You should be able to solve this to find some function of $\displaystyle t$.
Then! You can use that other part of the question...
That part is known as the initial conditions. You plug the $\displaystyle t$ value into the formula you found and solve it based on the value it tells you it should be.
So lets say, for example, [THIS IS NOT THE ANSWER.]
You solved the above and found that...
$\displaystyle x(t) = 3t^2 + c$
You're given at the start of the question that $\displaystyle x = 12$ when $\displaystyle t = 0$.
Hence plug $\displaystyle t$ into $\displaystyle x(t)$ and you get $\displaystyle x(0) = 0 + c = 12$, hence $\displaystyle c = 12$.
You will have to do the same except you will also need to find the derivative and sub in $\displaystyle t=0$ to that.