Homework Statement
Solve y''+4y'+5y=0
find solutions for y(0)=1 and y'(0)=0
Homework Equations
Quadratic equation
The Attempt at a Solution
Hows this look ?
assume solution is in the form of y=ce^{rx}
substitute y=ce^{rx} into the equation...
The integrating factor is e^{\int{\frac{2}{x}dx} = x^2
We than use this and multiply both sides by x^2
which gives
x^2y'+2xy = 3
or
yx^2= 3x+C
divide both sides by x^2
y = \frac{3}{x}+\frac{C}{x^2}
But isn't the justification that if K >0 and
K\phi(x, y) is a metric that's non negative
That it can't be > \frac{K\phi(x, z)}{1+K\phi(x, z)} + \frac{K\phi(z, y)}{1+K\phi(z, y)}?
You've got that the denominator = at least 1. So if x = z the function is 0.
Homework Statement
Assuming the maximum electric field sustained by dry air in a cloud is 3x10^6 Vm^-1
And a distanceof 1000 meters between Earth and cloud. The cloud is 4km long and 1 km wide. ausume uniform eletric field. Find the potential difference.
Homework Equations
V=Ed
\mu =...
Thanks for your help guys. In my textbook is says that the quotient topology is the finest. However in my tutorials when ever they talked about quotient topologies they always mentioned something about an equivalence relation. I think this question was meant to make me think about it which I...
I hope this clears it up. Sorry I'm not to good at latex.
Let(X,\phi)be a metric space. Take K > 0 and define.
\theta : X \cross X \rightarrow \real_{0}^{+},(x,y)\rightarrow\frac{K\phi(x,y)}{1+K\phi(x,y)}
show that (X,\theta)is a metric
so the triangle inequality
\theta(x,y)...
Yeah your right it is a typo the metric space should be (X,\phi)
so triangle inequality is
\phi(x,y) \leq \frac{K\phi(x,)}{1+K\phi(x,y)}
\leq \mid \frac{K\phi(x,z)}{1+K\phi(x,z)}\mid + \mid \frac{K\phi(z,y)}{1+K\phi(z,y)}\mid
= \mid \frac{K\phi(x,z)}{1+K\phi(x,z)} +...
Homework Statement
In a camera flash unit, a capacitor is charged up over a period of several seconds (from a battery). The capacitor is discharged very rapidly -- in about 1 millisecond -- into a gas tube producing a very brief, bright flash of light. How long will it take to charge a 195...
Hi guy's I know this is more of a homework question, I posted a similar thread earlier on but I think I ended up confusing myself.
I need to show that a function is continuous between metric spaces. I'll post the question and what I've done any tips on moving forward would be great.
I...
Does this look alright ?
I've tried to use Open balls of radius \delta and \psi
So I have three metric spaces
(X,\rho)
(X,\bar\rho)
and
(Y, \theta)
and a function
f : X \rightarrow Y
which is continuous wrt (X,\rho)
So given f : X \rightarrow Y continous wrt \rho...
Thanks for your help.
I have also got to prove the following
Let (Y, \theta) be a metric space. Prove the following.
f : X \rightarrow Y is continuous with respect to \bar\rho if and only if it is continuous with respect to \rho
I know I have to show that the inverse of Open sets in...