I've been given the ODE:
x^2 u''-x (x u'-u)=0
Solve.
It's suppose to be an example in which a logarithmic term is required for the general solution.
I would be glad if someone could look at what I've done and see if my solution is correct / incorrect.
Thank you in advance for your time...
W'=-2u2+2vu3<0
v>0, u<0 no problem
v<0, u>0 no problem
u,v both positive or both negitive are problematic because W' can be positive in those regions, no ?
sorry I forgot to mention I only had difficulty with the second part of the question.
W'= 2uu'+2vv'=2u[v-u]+2v[u(u2-1)]=2vu-2u2+2vu3-2uv
W' = -2u2+2vu3
I think (but perhaps I'm mistaken) W is suppose to be a lyoponouv function and I'm suppose to find the radius R in which W is monotically...
Given the ODE system:
v' = u(u2-1)
u' = v-u
Define w=u2+v2. Compute w'.
Find the largest radius R for which u2+v2<R so that the if the solution curve (u,v) is inside that circle the solution tends to (0,0) as t--> +\infty
Any guidance would be appriciated !
Homework Statement
A current loop (of circular shape) is located at the X-Y plane.
What is the magnetic field on the Z axis? (Use the magnetic moment and magnetic potential)
Homework Equations
M=(Ia)/c \widehat{z}
A=(MXr)/r^{3}
B=curl(A)
The Attempt at a Solution
I got that the...