Hi,
The problem is to solve:
dy/dx = −[2x + ln(y)]*(y/x)
Attempt:
I have tried to see if it is exact, I found it not to be, I can't easily find a function to multiply by to make it exact either (unless I am missing something obvious). It clearly isn't seperable, nor is it homogenous (I know...
Problem:
Express the quadratic form:
q=x1x2+x1x3+x2x3
in canonical form using Lagrange's Method/Algorithm
Attempt:
Not really applicable in this case due to the nature of my question
The answer is as follows:
Using the change of variables:
x1=y1+y2
x2=y1-y2
x3=y3
Indeed you get...
Problem:
Let f ∶ V → V be a linear operator on a finite-dimensional vector space V .
Prove that the sequence 0 → ker(f) → V → im(f) → 0 is exact at each term.
Attempt:
If I call:
a: 0 → ker(f),
b: ker(f) → V,
c: V → im(f),
d: im(f) → 0.
Then the sequence is exact at:
ker(f) if...
Problem:
y'=((x-1)/(x^2))*(y^2) , y(1)=1 . Find solutions satisfying the initial condition, and determine the intervals where they exist and where they are unique.
Attempt at solution:
Let f(x,y)=((x-1)/(x^2))*(y^2), which is continuous near any (x0,y0) provided x0≠0 so a solution with y(x0)=y0...
Sorry I have just looked over my notes and realized that I wrote: "two people are holding the plank at either end they move further apart", so it must mean they are just walking back". I'll edit it on the first post now
I think the teacher was just trying to use an analogy to make it easier to understand. I am just in the process of creating images, which I will upload in a second.
Homework Statement
"Two people are holding a plank of wood at either end, with a mass located at the halfway point between them, they both walk backwards extending their arms, the mass still being halfway between them. The plank becomes harder to support, why is this?"
Homework Equations
Maybe...
Homework Statement
We were shown this image ^
We were later told that it is suggested that the depression (y), is directly proportional to the length of the beam cubed (L3). We were asked to give reasons why this is so.
EDIT: The 1kg mass is placed at L/2
Homework Equations
y is directly...
Homework Statement
Question: "The midpoint of a guitar string oscillates with an amplitude of 2.24mm with a frequency of 400Hz. Calculate:
i) The maximum speed at this point
ii) The maximum acceleration of the string at this point"
Homework Equations
Suitable formulas: x=Asin(2*pi*f*t) ...