Can someone tell me if I did this right because my solution seems wrong, but I've done it a couple times and get the same answer. I'm given the following:
x' + 2y' + x = 0
x' - y' + y = 1
and the initial values of x(0) = 0 and y(0) = 1
The idea is to solve this initial value problem.
Can...
I was wondering if anyone could check my work on this to make sure I'm doing this right for finding a particular solution to y''' + 3y'' + 3y' + y = e^(-x) + 1 + x. First I split the problem into 2 halfs y_p1 and y_p2.
y_p1 = Ce^(-x)
-Ce^(-x) + 3Ce^(-x) - 3Ce^(-x) + Ce^(-x) = e^(-x)...
o da, thanks... okay, so I get (r+1)^3 = 0. Now for my general solution I get
y(x) = c1(e^-x) + c2x(e^-x) + c3(x^2)(e^-x). How do I figure out the 3 linearly independent solutions?
yes y^(3) is supposed to be y''' I was told that after y'' your supposed to use y^(n). As for the characteristic function I'm getting
r(r^2 + 3r + 3) + 1 = 0. I'm not sure how to break it down after that.
I'm having trouble understanding what to do for this problem. The question I'm trying to answer is: Find 3 linearly independent solutions to the following differential equation, y^(3) + 3y'' + 3y' + y = 0. I really don't know how to even start this problem and what I'm really looking for. I...
I'm stuck on what to do here. The question reads Consider a population P(t) satisfying the logistic equation dP/dt = aP-bP^2, where B = aP is the time rate at which births occur and D = bP^2 is the rate at which deaths occer. If the intial population is P(0) = P_0 (supposed to be P sub not)...
I'm trying to solve this problem and I can get one part but not the other. Here is the information I was given: A uniform, cylindrical pulley of mass M=3.30 kg and radius R=0.660 m rotates freely about a fixed horizontal axis. A block which moves downward is attached to a string of tension...