Recent content by tylersmith7690

Homework Statement In attatchment Homework Equations Not sure How to come up with the other equations. The Attempt at a Solution Assuming a node is an element connected to two or more elements. 1) Moving clockwise from V i1 to i2. Node one is between the negative side of the...

1/ (y-sinx) = -sinx/2 + C cosx = (-sinx +2 C cos x)/2 y-sinx = 2/(-sinx +2 C cos x) y= 2/(-sinx +2 C cos x) +sin x y= [2 + sinx ( 2 cosx - sin x)]/ 2 cos x - sin x y = (2 + 2 C sin x cos x -sin^2 x ) / ( 2 cos x - sin x) y= 2+ C sin 2x - sin^2x / 2 cos x - sinx This...

Homework Statement The simplest useful model for fisher comes from the logistic model for population growth, together with a harvest h which is proportional to the current population P, that is, h=EP, where the constant E is called the effort. E measures the fraction of the population...

I don't see how you get y by itself. Maybe my algebra is way off. And i believe the RHS should have a negative before the 1/2 sin x. Any help would be welcomed.

Homework Statement For the following differential equation: dy/dx = \frac{2cos^2x-sin^2x+y^2}{2 cosx} , -pi/2 < x < pi/2 show that the substitution y(x)=sin x + 1/u(x) yeilds the differential equation for u(x), du/dx = -u tan x - \frac{1}{2}sec x Hence find the solution y(x) to...

Yeah looking back i see the trick is just to square the ((1/-3i_2))

Homework Statement Using the complex exponential, nd the most general function f such that \frac{d^2f}{dt^2} = e-3t cos 2t , t all real numbers. Homework Equations I'm having a lot of trouble with this question, my thinking is to integrate once and then one more time...

Is my final answer correct? x + \frac{9}{8} log | x2+4 | - \frac{9}{4} arctan(\frac{x}{2}) - \frac{1}{4} log | x-2 | + C

Thanks for the reply, looking again at how i got C=0 was most likely due to it being very late at night :). But yes I find it easier solving for A,B,C in the system of equations. I see now that my thinking was on the right track and it was just the small error that through me off. Thanks for the...

Integral help! Homework Statement Evaluate the following indenite integral, ∫\frac{x^3-5x}{x^3-2x^2+4x-8} dx Homework Equations I think I am right until i get to equating the equations when I do it the method I am taught in class I get c=0 and I don't think that is right. However when...

Homework Statement Sorry for the poor use of Latex, I have tried to get it to work but it seems to never come out as I would like. Using a trigonometric or hyperbolic substitution, evaluate the following indfenite integral, ∫\frac{1}{\sqrt{(x^2-1)^5}} dx Homework Equations I...

would i use the l'hopital rule in my working out? and what is the usual expansion?

So if I end up with log(1) = 0, Would that mean I was right? or do i have to do some algebra first to solve the stuff inside the bracket?

Sorry for the headache, my second attempt above at working out had a + instead of a - after the first x in the bracket. It should read (x-1 + ...)/x Because the function log is continuous. we get limx→0+ (\frac{x-1+\sqrt{}x^2+1}{x}) = \frac{0-1+1}{0} which is \frac{0}{0} indeterminate form...

Would i make the original equationin into limx→0+ log ((x-1+\sqrt{x^2+1})/x)) = limx→0+ log( 1 - \frac{1}{x} + \frac{\sqrt{x^2+1}}{x}) And then can i say that because log is continuous when x>0, that i can then put log(limx→0+ 1 - limx→0+\frac{1}{x} + lim x→0+ \frac{\sqrt{x^2+1}}{x})...