# differential

1. ### Differential Integration Problem

Attempt at solution: Writing the chain rule for $E(V,T)$: $dE = \frac{\partial E}{\partial T}dT + \frac{\partial E}{\partial V}dV$ Then, integrating the differential: $\int{ dE } = \int{ \frac{\partial E}{\partial T}dT } + \int{ \frac{\partial E}{\partial V}dV }$ If I put the...
2. ### I X variable in damping force equation for damped oscillation?

Hi, for ease of reference this posting is segmented into : 1. Background 2. Focus 3. Question 1. Background: Regarding (one, linear, second-order, homogeneous, ordinary, differential) equation describing the force in a non-driven, damped oscillation: F = m.a = -k.x - b.v F =...

7. ### I Christoffel symbols knowing Line Element (check my result)

Hi! I'm asked to find all the non-zero Christoffel symbols given the following line element: ds^2=2x^2dx^2+y^4dy^2+2xy^2dxdy The result I have obtained is that the only non-zero component of the Christoffel symbols is: \Gamma^x_{xx}=\frac{1}{x} Is this correct? MY PROCEDURE HAS BEEN: the...
8. ### Differential Equations: Solve the following

1. Homework Statement Solve the following differential equations/initial value problems: (cosx) y' + (sinx) y = sin2x 2. Homework Equations I've been attempting to use the trig ID sin2x = 2sinxcosx. I am also trying to solve this problem by using p(x)/P(x) and Q(x) 3. The Attempt at a...
9. ### Differential Equations, solve the following: y^(4) - y'' - 2y' +2y = 0

1. Homework Statement Solve the following differential equations/initial value problem: y^(4) - y'' - 2y' +2y = 0 Hint: e^-x sinx is a solution 2. Homework Equations I was attempting to solve this problem by using a characteristic equation. 3. The Attempt at a Solution y'''' -y'' -2y' +...
10. ### I Heat equation plus a constant

I have seen how to solve the heat equation: $$\frac{ \partial^2 u(x,t) }{\partial x^2} = k^2 \frac{ \partial u(x,t) }{\partial t}$$ With boundary conditions. I use separation variables to find the result, but i dont know how to solve the equation plus a...
11. ### How to calculate total cross section from differential cross section

I was doing the calculations for this: http://fermi.la.asu.edu/PHY531/cylinder/index.html But I can't figure out how to go from \frac{d\sigma}{d\phi} to the total cross section. My guess was that you did the integral from \phi=0 to \phi=2\pi, but that's not helping since I can't tell either how...

21. ### Properties of Solutions of Matrix ODEs

1. Homework Statement We assume from ODE theory that given a smooth A: I → gl(n;R) there exists a unique smooth solution F : I → gl(n;R), defined on the same interval I on which A is defined, of the initial value problem F' = FA and F(t0) = F0 ∈ gl(n;R) given. (i) Show that two solutions Fi...
22. ### Frenet Frame

1. Homework Statement The Frenet frame of a curve in R 3 . For a regular plane curve (and more generally for a regular curve on a 2-dimensional surface - e.g. the 2-sphere above) we could construct a unique adapted frame F. This is not the case for curves in higher dimensional spaces. Besides...
23. ### Various Properties of Space Curve...*Really need help*

1. Homework Statement Let γ : I → R3 be an arclength parametrized curve whose image lies in the 2-sphere S2 , i.e. ||γ(t)||2 = 1 for all t ∈ I. Consider the “moving basis” {T, γ × T, γ} where T = γ'. (i) Writing the moving basis as a 3 × 3 matrix F := (T, γ × T, γ) (where we think of T and...
24. ### Find A and B so that F(x) is a Differentiable Function

1. Homework Statement Find the values of a and b that make f a differentiable function. Note: F(x) is a piecewise function f(x): Ax^2 - Bx, X ≤ 1 Alnx + B, X > 1 2. Homework Equations 3. The Attempt at a Solution Made the two equations equal each other. Ax^2 - Bx = Alnx + B Inserting x=1...
25. ### Proving basic linear ODE results

1. Homework Statement Please bear with the length of this post, I'm taking it one step at a time starting with i) Let A: I → gl(n, R) be a smooth function where I ⊂ R is an interval and gl(n, R) denotes the vector space of all n × n matrices. (i) If F : I → gl(n, R) satisfies the matrix ODE...
26. ### Differentiation question

1. Homework Statement Summarizing: two civilizations hate each other, one of the civilizations throws a curse at the second. The second civilization succumbs to chaos and has a change in Population each week of ΔP= -√P. That is: Pn = Pn-1-√Pn-1 2. Homework Equations Considering that the...
27. ### Where is wrong in this proof for rotational inertia ?

1. Homework Statement Prove the formula for inertia of a ring (2D circle) about its central axis. 2. Homework Equations I = MR^2 Where: M: total mass of the ring R: radius of the ring 3. The Attempt at a Solution - So I need to prove the formula above. - First, I divide the ring...
28. ### 2nd Order Linear ODE-Derivation of system-issue

1. Homework Statement How exactly they combined equation1 and equation2 and got that system? I don't get that part. 2. Homework Equations A*(dy/dt)= -k*y eq1 A*(dz/dt)=ky-kz eq2 3. The Attempt at a Solution I tried substituting the 1st ky in the 2nd equation and then differentiating but...
29. ### Analysis Books on solving DE with infinite series?

Hi folks, I was wondering if there are books that explain how to solve differential equations using infinite series. I know it is possible to do it since Poincaré used that method. Do you know which ones are the best? I find books on infinite series but they talk just about series...
30. ### Matrix riccati differential equation using matlab

1. Homework Statement 2. Homework Equations 3. The Attempt at a Solution