# Search results

1. ### Solution to general IVP

Bump...any suggestions?
2. ### Solution to general IVP

Homework Statement Find all solutions of the IVP y'' + a(t)y' + b(t)y = 0, y(t0) = 0, y'(t0) = 0 where t0 is any fixed point on the t-axis and the coefficients are continuous. The Attempt at a Solution I know this has to do with the Existence and Uniqueness theorem. How would I apply...
3. ### Differential Equations - Exponential Decay

These are what I think I'm not sure how to find graph solutions from my equation: y = 4 + Ce^(-.5t) Thanks for your help!
4. ### Differential Equations - Exponential Decay

So...first interval - exponentially decreasing graph when y = R/k, it's a constant, straight line along R/k? and when y is big, it's increasing?
5. ### Differential Equations - Exponential Decay

Homework Statement We have the ODE y' = -ky + R for a population y(t) where death rate exceeds birth rate, counteracted by a constant restocking rate. I'm assuming k is the decay constant and R is the restocking rate The population at time t0 = 0 is y0, and I have to find a formula for...
6. ### Line Integral

Ok thanks! But what if it's something like F(x,y,z)=(xy, x/z, y/z) ? Then if you plug in 0, you get a denominator of zero...
7. ### Line Integral

Homework Statement What is the line integral of F(x,y,z) = (xy, x, xyz) over the unit circle c(t) = (cost, sint) t E (0,2pi) ? Homework Equations integral= (f(c(t))*c'(t))dt) The Attempt at a Solution Ok, so I tried solving this like I would any other line integral using the given...
8. ### Integration of a function.

ohh....but how is the triple integral from 0 to 4-x^2-y^2 ? I know it's the function, but graphically, I don't understand. Oh well, my homework was due 10 minutes ago and I just turned it in (leaving this question blank) lol. Thanks for the answer though!
9. ### Integration of a function.

Homework Statement Hey guys, I have one question: how can I integrate the function f(x,y,z)=x + y + z over the region between the paraboloid 4-x^2-y^2 and the xy-plane? Homework Equations For the paraboloid region, I used polar coordinates and found the volume of the region to be 8pi...
10. ### Volume of region R between paraboloid and xy-plane

Alright, I used polar coordinates, i think, I got 8pi.
11. ### Volume of region R between paraboloid and xy-plane

Would it be plus/minus sqrt(4-x^2) ?
12. ### Volume of region R between paraboloid and xy-plane

Ok, for my limits, i got x is between 0 and 2, and y is between 0 and 2...so i did a double integral and got 16/3. Is that right?

14. ### 4-ball B^4

Homework Statement What is the x-simple description of a 4-ball = { ||x|| \leq r } Homework Equations It's a 4-ball, so isn't the equation x^{2} + y^2 +z^2 +w^2 ? The Attempt at a Solution For my limits, I got x is between \pm \sqrt{1-z^2} and y is between -1 and 1, and z is...
15. ### Volume of region R between paraboloid and xy-plane

Umm, isn't the equation just z=4-x^2-y^2 ? Ok, thanks, I'll try a double integral, so for the limits, I would just set z=0, right? and solve for x and y?
16. ### Volume of region R between paraboloid and xy-plane

Homework Statement So my question is: what is the volume of the region R between the paraboloid 4-x^2-y^2 and the xy-plane? Homework Equations I know how to solve it, it is a triple integral, but how do you find the limits of integration? The Attempt at a Solution Do I set x=0...