Recent content by NCyellow

thanks guy! I can't believe i didn't see that!

Homework Statement Find a fundamental set of real solutions of the system. x'=[-0.5 1 ]x [-1 -0.5] The Attempt at a Solution I calculated the eigenvalues to be r1 = -0.5+i and r2 = -0.5-i Then, attempting to calculate the eigenvectors, I plugged the numbers into the system...

I'm sorry, how did you get that equation?

Homework Statement Given the following differential equation t^3y''' - t^2y'' + 2ty' - 2y = 0; t > 0 Find a solution that satisfies differential equation and the initial conditions y(1) = 3; y'(1) = 2; y''(1) = 1 Homework Equations The Attempt at a Solution I tried plugging in...

Hi, Thank you so much for helping me. I will try to be more clear in the future.

Hi, thank you very much. I guess i misread a rule from the book when I thought that differentiating it would be simple. When i said plugging numbers in I meant plugging the y and y' back into the original equation to make sure it works.

Yes, but the first e^(t^2) is outside and multiplying the integral.

Wrote the signs wrong, fixed now.

Homework Statement I am given dy/dt -2yt = 1 and y(t) = (e^(t^2))[e^(-s^2)ds] + e^(t^2) integrate from t to 0 within the brackets. Homework Equations The Attempt at a Solution I know that the derivative of y(t) would equal e^(t^2) However I do not know how I am supposed to solve...

Homework Statement The problem is given as follows: Solve dy/dt + y = 0.5, y(t=0)=1Homework Equations The Attempt at a Solution I separate the y terms from the t terms, which gives me dy(-y+0.5)=dt I integrate both sides to get -ln(-y+0.5)=t+C C is the constant, I combine the constants from...

I went back to look in my textbook, but I am still confused by what you mean. I know that d is the separation between slits, D is the actual width of each slit, and theta is the angular spread. I am still confused however.

Homework Statement Missing orders occur for a diffraction grating when a diffraction minimum coincides with an interference maximum. Let D be the width of each slit and d the separation of slits. (a) show that if d = 2D, all even orders (m=2,4,6) are missing. (b) show that there will be...

Homework Statement A bulb emits a continuous spectrum of ultraviolet, visible and infrared light in the wavelength range 360nm to 2000nm. Assume that the light from this bulb is incident on a diffraction grating with slit spacing d and that the first-order brightness maximum for the wavelength...

well, derivative of e^4x is 4e^4x. So that must be an element of the entire answer. So it will be (something)(4e^4x). But how do you go about deriving the first run?

With chain rule, is it 4(e^4)?