I tried diffrentiating upto certain higher orders but didn’t find any way.. is there a trick or a transformation involved to make this task less hectic? Pls help
Homework Statement
This problem is from V.I Arnold's book Mathematics of Classical Mechanics.
Q) Show that every differential 1-form on line is differential of some function
Homework Equations
The differential of any function is
$$df_{x}(\psi): TM_{x} \rightarrow R$$
The Attempt at a Solution...
So there's this question I've to do. I got through until a certain point and now I'm stuck. >->
1&2The question:
The rate of deterioration of a product in a container is proportional to the amount of product present. At time t, the amount of product is x.
(i) State the diffrential equation...
hi, Initially, I know how to take surface integral of möbius band via given parameterization, but I really wonder how these parameters are created. How can we derive these parameters ?? What is the logic of deriving such a good parameters?? Could you give some proofs??
1. I need to find a condition that the equation will have a integration factor from the shape K(x*y).
(K-integration factor sign)
2.the eq from the shape M(x,y)dx+N(x,y)dy=0 ,not have to be exact!3. i tried to open from the basics. d(k(x*y)M(x,y))/dy=d((k(x*y)N(x,y))/dx.
and i used the fact...
Homework Statement
Good day all,
My professor gave my class a packet of about 40 differential equations.
I for the life of me cannot figure out how t solve these last 4!
I also have an exam tomorrow morning, and would like finish these last few.
I don't need them solved out, I would just...
Homework Statement
There are now about 3300 different human "language families" in the whole world. Assume that all these are derived from a single original language, and that a language family develops into 1.58 language families every 5860 years. About how long ago was the single original...
hi.
Is there something wrong in using the Frobenius method for regular singular point while solving Legendre's differential equation (expanding about x=0)?
Though the solution of Legendre Differential Equation here- http://mathworld.wolfram.com/LegendreDifferentialEquation.html
uses the...
Hey
Not done this in ages and just can't figure it out, i need to solve the equation;
\frac{dv}{dt}=-\alpha v+\lambda F
Where alpha,lambda and F are constants.
I'm so used to solving differential equations numerically i think I have forgotten how to do it analytically:P
My first attempt...
Hello,
I managed to solve the differential equation : dx/dt= 0.1 (x-250)
with the information when t=0 x=1000 and dx/dt= 75, I also found "C" and got
ln lx-250l = 0.1t + ln750
However, I am having trouble obtaining the expression for x in terms of t
I got x= e^0.1t +1000 which...
Homework Statement
hey, it's been on my wish list for some time, i have decided to teach my self diffrential equal, rather than waiting to be taught at school, after having some exposure through vibrations and circuits.
so i got a book and i started to learn, the question came to be...
Homework Statement
r''-(theta')^2=-g reads: second derivative of r minus the first derivative of theta squared equals negative g
2(r')theta'+(r)theta''=0 reads: 2 times the first derivative of r times the first derivative of theta plus r times the second derivative of theta.
both r and...
Hey, in my textbook they keep doing this and I can't follow
for example r.\ddot{}r = 1/2 \ddot{}r^{}^2{}
and r.\dot{}r = 1/2 \dot{}r^2{}.
Can anyone explain this to me? I know I should probably know it.
P.S Can't quite get the dot product to look right apologies.
Homework Statement
let x + y = u and y = uv
Expand dx and dy in terms of du and dv
Homework Equations
The Attempt at a Solution
i got this answer:
dy = udv + vdu
and
dx = du - udv - vdu
is this correct?
hi all
this is the general problem
X\ddot{}+AX\dot{}+BX=0
let A, B,X be 2*2 matrices
its application is in vibrations.
any opinion will be great
I can solve the first-order but ...
Homework Statement
Two cars approach an intersection at the same time. The red car is 300m east of the intersection and traveling at a speed of 60km/h. The blue car is 450m north of the intersection and traveling at a speed of 75km/h. When are the two cars the closest?
Homework...
Problem with an easy diffrential equation, the problem is explained in the picture ...
http://img209.imageshack.us/img209/7341/diffproblemsf9.jpg
Kindly TNS