What is Diffrential: Definition and 19 Discussions

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1. Change in the time period of a pendulum

I tried taking log and then diffrentiate the standard equation for time period of a pendulum but i am not getting the correct answer
2. Is There a Trick to Simplify Taylor Series Expansion?

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
3. Is Every Differential 1-Form on a Line the Differential of Some Function?

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...
4. Math modelling diffrential equation question?

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...
5. A Möbius band diffrential geometry

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??
6. Diffrential equations, integration factor with two vars

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...
7. Help Differential Equations types

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...
8. Language growth with diffrential equations.

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...
9. Help with solution of legendre's diffrential equation.

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...
10. Can't figure out how to solve a diffrential equation

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...
11. Diffrential equation subject qs

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...
12. How Do You Solve This Differential Equation: $$x^3 \frac{dy}{dx} = y$$?

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...
13. Solving a system of 2 diffrential equations with 3 unknowns.

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...
14. Scalar Product of a diffrential.

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.
15. Still stuck on diffrential equations

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?
16. How to Solve a Differential Equation with Nonlinear Terms?

solve the diffrential equation: xy' = x(e^(-y/x)) + y answer: y = xln|lncx| problem: i don't get it can anyone explain
17. How to solve second-order matrix diffrential equation?

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 ...
18. Diffrential calculus; distance problem

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...
19. Problem with easy diffrential equation

Problem with an easy diffrential equation, the problem is explained in the picture ... http://img209.imageshack.us/img209/7341/diffproblemsf9.jpg Kindly TNS