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...