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...
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...
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...
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!
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...
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...
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?
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...
Homework Statement
Find the equation of the plane through vectors u=(1,1,2) parallel to the plane containing v=(2,2,-1), w=(1,-1,0), and the origin.
Homework Equations
The Attempt at a Solution
I did the cross product of v x w = (-1,-1,-4).
Thus, my equation became -x-y-4z=-9...