Recent content by bitrex

Thanks for your reply, I'm not sure exactly why I thought they were satisfied either! I see now that they are not. A further question - some exercises in the problem set I'm working on ask me to determine where a complex function is differentiable, and some to determine where the function is...

I'm doing a little self study on complex analysis, and am having some trouble with a concept. From Wikipedia: "In mathematics, the Cauchy–Riemann differential equations in complex analysis, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential...

I don't see where I made that substitution? I now see I did make an error on this line:C_1\int \frac{1}{2} + \frac{cos2\theta}{2}d\theta = C_1(\frac{\theta}{2} + sin\theta cos\theta + C_2) The integral of \frac{cos(2\theta)}{2} = \frac{sin(2\theta)}{4} , which I then replaced with a...

Homework Statement Use the substitution y = (x^2 + 1)u to solve the differential equation (x^2 +1)y\prime\prime = 2y The Attempt at a Solution I was having some trouble with these earlier because I needed to brush up on my trigonometric substitution. Let's try this one... Making the...

I see it now. It's been months since I've worked on this stuff, and as you can tell I'm pretty out of practice. Ugly careless mistakes. :frown:

I think I'm a little closer now. Continuing from the dropped constant and substituting into p = dx/dt we have: \frac{1}{\sqrt{C_1 - \omega^2 x^2}} dx = dt Make the substitution x = \frac{\sqrt{C_1}}{\omega} sin\theta \int \frac{\sqrt{C_1} cos\theta}{\omega C_1 cos\theta} d\theta...

Carelessness. I'll try it again.

To finish up: p dp = -\omega^2x dx p^2 = -\omega^2 x^2 p = i \omega x + C_1 t = \int \frac{1}{i\omega x + C_1} dx i \omega t = ln|i\omega x + C_1| + C_2 e^{i\omega t} = C_2(i\omega x + C_1) = C_2x + C_1C_2 \frac{1}{C_2}cos(\omega t) + \frac{1}{C_2}isin(\omega t) - C_1 x...

:smile: :cry: Wow, so I do. That's what I get for doing this when I'm tired!

Homework Statement Substitute p = \frac{dx}{dt} to solve x\prime\prime + \omega^2x = 0 Homework Equations \frac{dp}{dx} = v + x\frac{dv}{dx} v = \frac{p}{x} The Attempt at a Solution p = \frac{dx}{dt}, \frac{dp}{dt} = \frac{d^2x}{dt^2} \frac{dp}{dt} = \frac{dp}{dx}\frac{dx}{dt} =...

Aha! I see it now. Need to remember my "exponential shift" rule. So we get \frac{s+\alpha-\alpha}{(s-\alpha)^2 + b^2} = \frac{s-\alpha}{(s-\alpha)^2 + b^2} + \frac{\alpha}{(s-\alpha)^2 + b^2} = e^{\alpha t}L^{-1}(\frac{s}{s^2+b^2} + \alpha\frac{1}{s^2+b^2}) which I believe is the Laplace...

Homework Statement Not a homework problem exactly, but in an EE textbook I saw something to the following effect: To obtain the time domain behavior for \frac{s}{s^2+\frac{\omega_0}{Q} + {\omega_0}^2} the following Laplace transforms are combined to cancel the term in the numerator...

I'm wondering if anyone knows how, using the Maxima CAS, to force the evaluation of an expression? For example, if a function returns something like the following as a solution: -\frac{{2}^{\frac{6}{4\,log\left( 2\right) -5}+2}-5\,\left( \frac{6}{4\,log\left( 2\right) -5}+2\right) }{log\left(...

I understand the rational for using the Lambert W. function for solving equations such as x^x = z , where no derivative in terms of elementary functions exists for the expression. However, on the Wikipedia page about the Lambert W. function, an example is given with the equation 2^t = 5t. In...

Yes, that's what went wrong. I forgot to put in the initial conditions properly! Thank you.