Recent content by darryw

Homework Statement When the two microphones are at the same distance from the speaker, the two signals are in phase. For the phase difference shown (the two waves are separated by .001ms) , and given your value for the speed of sound(330m/s) , what is the minimum distance between the two...

next part asks about linear independence, but i already know this is just making sure wronskian doesn't equal zero. thanks for all the help

it was property of exponents that was problem.. wow. so y_2 = root t is also a solution (1/4t) - (1/4t) = 0

hang on sec.. i see something stupid

y(t) = t^(1/2) y'(t) = (1/2)t^(-1/2) y''(t) = (1/4)t^(-3/2) plug into equation.. t^(1/2)((1/4)t^(-3/2) + ( (1/2)t^(-1/2))^2 (1/2)t^(-1) + (1/4)t^(1/4) thanks

Homework Statement Is y_1 = 1 and y_2 = root t solutions of the eqn: yy'' + (y')^2 = 0 ? first solution works (i already verified) 2nd solution i get this: (1/2)t^(-1) + (1/4)t^(1/4) which does not equal zero. is this correct so far? the thing that confuses me is the question...

thanks psholtx. isn't it already proved by saying that if (∂M/∂y - ∂N/∂x)/N = f(x) then e∫f(x) dx is an integrating factor. If that is true, then wouldn't integrating N_x to show exactness be redundant?

i now need to integrate wrt x, xe^x (x + 2) cos y first i simplify the x's into 2 terms: x^2e^x + 2xe^x integrate wrt x using integ by parts on both terms e^x(x^2 - 2x + 2) + 2xe^x -2e^x then add the y term [e^x(x^2 - 2x + 2) + 2xe^x -2e^x ]cos y + h(y) then take partial derivative of...

I am asking if that is valid, because if i come across something a lot more difficult (time consuming) to differentiate, i can just note that M_y must = N_x and proceed without actually differentiating N_x, right? thanks

multiply everything by integ factor, xe^x... xe^x[ (x + 2) sin y dx + x cos y dy ] = 0 ...M......N M_y = xe^x (x + 2) cos y N_y = xe^x (x + 2) cos y since I've already determined the integ factor that makes equation exact, N_y must be the same as M_y, so it isn't necessary to...

wow that is useful. so i have [(x+2) cos y - cos y] / xcos y = ? simplify... (cos y's cancel) (x+2)/x - (1/x) = x+1/x = 1 + 1/x so integrating factor, mu(x) is e^integ (1+1/x) e^x+ln|x| simplifies to: xe^x so my integrating factor is mu(x) = xe^x correct so...

ok thank you, but i am still confused as to how to actually get the integrating factor? (to make an equation exact)??

I am familiar with getting integrating factor by putting equation in the form y' + p(t)y = g(t) and so integrating factor is mu(x) = e^integ p(t)dt. but i am not familiar with using an integrating factor to make an equation exact? isn't my goal to multiply the equation by some factor to make...

thanks.. actually i am already stuck. I do know i need an integrating factor but i don't know steps to get one. I could start by multiplying whole equation by x, but isn't this just random guessing? I also know that my goal is to make DE exact by finding correct integ factor, and then i can...

thanks for the explanation. My final answer is now matching answer key, so I am moving on to my other prob.. thanks.