I think the two different solutions have to be independent of each other - or not be multiples of each other. I'll give it a shot and see what happens though. Thanks.
Here's the problem:
x^2y''-3xy'-12y=0
with initial conditions y(1)=0 and y'(1)=7
I'm supposed to solve for y in the form y=c1y1+c2y2
y1 = x^6 by inspection
Now to solve for y2
y2=y1v
v can be solved for by the equation
y1v''+(2y1'+py1)v'=0
where p is the function in front...
Crap, nevermind, I left b^2 out of the quadratic formula, thanks anyways.
Here's the question:
Find y as a function of t from the diff eq:
y''+6y'+25y=0 with the initial conditions y(0)=8 and y'(0)=8
I used the form r^2+6r+25=0 to solve for r and through the quadratic equation got r =...
For the first question you should draw a freebody diagram and from there you can get the net force acting on the sphere: buoyant force - weight.
For the second question I think the circular diameter is best described by a donut, from the inside to the outside is 5.6 mm. The total weight of...
Here's the question:
A particles position is defined by the equation x=y^2/6 and it moves at a constant velocity in the y-direction of 3 in/s. Find the velocity and acceleration when x=6 in.
I know v=sqrt(vx^2+vy^2) and a is found the same way, but I have absolutely no idea how to find the...
Never mind, I figured it out.
Here's the question:
Find the general solution to the homogeneous differential equation
https://webwork.math.uga.edu/webwork2_files/tmp/equations/59/540a7a16e5c4e841a098d9d2a72f0a1.png
The solution has the form...
I'm supposed to find the deflection of a beam. It's steel with a brass shell, so they have different values for E. How do I do this problem using PL/AE.
Intuitively I think I should take the average, but I have no idea if that's right or not.
Thanks.
I should probably give some more...
OK I lied, I'm still not getting the right answer.
dP/P(7-P)=6/700dt
1/7log(P)-1/7log(7-P)=6t/700+c
log(P)-log(7-P)=6t/100+c
Using e
P-7+P=e^(6t/100)+c
P=(e^(6t/100)+7)/2+c
P(0)=3 so c=-1
Subbing 66 for t, I get 28.729
Still not right, what am I doing wrong now?
Thanks again.
Here is the first question:
A population P obeys the logistic model. It satisfies the equation
https://webwork.math.uga.edu/webwork2_files/tmp/equations/11/02d0a645c053f1f6002d746c78143f1.png
Assume that P(0)=3. Find P(66)
First I multiplied both sides by dt and integrated, giving...
I have the equation A
44*e^(kt/5)+49((1-e^(kt/5))/k)
and I'm supposed to evaluate as k-->0
I think I'm supposed to apply l'hospital's rule to the second part of the equation, which would give
49*((1-t/5*e^(kt/5))/1)
which as k-->0 is
49*(1-t/5)
so the whole thing as k-->0 is...
I already found this equation:
T= 15/1.36(.6*sin(t)-cos(t))+100-23.971/e^(.6t)
Now I'm supposed to find the range of temperatures (T) as t approaches infinity.
I tried 100+(15/1.36*.6*sin(90))
and 100-(15/1.36*cos(0))
but that's not right. What am I missing?
Thanks.
Here's the question:
A bacteria culture starts with 820 bacteria and grows at a rate proportional to its size. After 3 hours there will be 2460 bacteria.
(a) Express the population after t hours as a function of t.
I tried y=y'+820, so -y'+y=820
p(t)=1
mu(t)=e^t
I carried this out...
Here's the question:
If the pressure of a substance is increased during a boiling process, will the temperature also increase or will it remain constant?
It seems like it would increase because boiling is basically the release of pressure to create equilibrium. Is this right?
Thanks a lot.
Here's the problem:
Solve y'-4y=9e^(7t) with y(0)=5
p(t)=-4
mu(t)=e^(int[-4dt])=e^(-4t)
multiplying both sides by mu(t)
e^(-4t)(y'-4y)=9e^(3t)
Dt(e^(-4t)y)=9e^(3t)
e^(-4t)y=3e^(3t)+c
y=(3e^(3t))/(e^(-4t))+c/e^(-4t)
now when y(0)=5
5=3+c
c=2
so y=(3e^(3t))/(e^(-4t))+2...
Hey guys,
Here's the question:
A point A moves along a curve with the equation x = y^2/6 and is elevated in the y direction at a constant velocity of 3 in/s. Calculate the velocity and the acceleration when x = 6 in.
So I solved for y and y=sqrt(6*x) and when x=6 y=6.
Since the...
I'm supposed to derive an equation that will find whether or not a point is inside or outside a shape with only the coordinates of the vertices given.
The shape is expected to be something like this:
______
|........|.........._____
|........|______|.......|...
Hey, I'm working on a project with RoboJDE and java and I have a few quick questions.
What I'm supposed to do is write code so that the camera will find the coordinates of a swatch of color and move accordingly as the swatch changes positions. The robot is supposed to move from side to side...
When t = 0 it is the highest (or lowest since it's negative) because e^0=1 so it's just -Q/RC
As t approaches infinity e^(-t/RC) will equal 0, so the extremes will be 0 and -Q/RC, right?
Is there a difference between that current and the current that's actually in the resistor?
Thanks.
Are the nodes at the resistors or at the intersections of the conducting wire? I checked out the wikipedia site but it's still not making a whole lot of sense to me.
Thanks.
Is it anything like (0-V1)/4 + (V1-V3)/8 + (V2-V4)/8 = 0A and V2 - V4 = 20V ?
with V1, V2, V3, V4 going...
Alright, I'm getting somewhere now but I'm not sure how many loops there are in this circuit. I think it's 5:
Loop 1: E1 to R1 to R2 to E1
Loop 2: E1 to R1 to R3 to E1
Loop 3: E1 to R1 to E2 to E1
Loop 4: E2 to R4 to R3 to E2
Loop 5: E2 to R4 to R2 to E2
Is this right?