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Differential Equations

- An equation involving derivatives of a function or functions. Solving ODE and PDE
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Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions...
Feb23-13 09:24 AM
micromass
1 25,855
My intent is to create a thread for people interested in Differential Equations. However, I will explicitly state that...
Jul3-12 07:18 PM
Luccas
95 121,257
For a system of linear differential equations with constant coefficients with known initial conditions an analytical...
T 10:26 AM
Mark44
1 78
I'm trying to analyze the following Ito stochastic differential equation: $$dX_t = \|X_t\|dW_t$$ where X_t,...
Y 06:57 PM
Only a Mirage
2 125
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Hi everyone, I'm taking the Differential Equations for the first time, and I want to know the most helpful textbook...
Y 08:12 AM
Bill_K
2 182
When I multiply out the first line I end up with an extra (dA/dx)*(dσ/dx). Can someone please show me how i get from...
Apr17-14 04:44 PM
Bill_K
1 125
I'm having a hard time understanding Green's functions which have been introduced quite early on in the course, and...
Apr17-14 01:55 PM
homeomorphic
1 81
In this video at around 9:00 , Carl Bender demonstrates a method of solving y''+a(x)y'+b(x)y=0. ...
Apr17-14 09:28 AM
chipotleaway
2 94
Definition: ##f(x+k) = \exp(k \frac{d}{dx}) f(x)## So I thought, how take advantage this definition? Maybe it be...
Apr17-14 08:19 AM
Jhenrique
2 135
Hello I am trying to solve this ODE dx/dt=(f(x)+g(t))^(1/2) I have been recalling what I learn in my ODE...
Apr16-14 02:16 PM
MathematicalPhysicist
8 195
On Wolfram Alpha it will offend give you a contour plot, and it has similarities to a bifurcation plot with respect to...
Apr15-14 10:57 PM
JonDrew
0 75
I tryied make the convolution product between x and x by ##\int_{- \infty}^{+ \infty} f(u) g(x-u) du## and the...
Apr14-14 06:20 PM
micromass
5 170
I have a differential equation to solve below on the motion of an object oscillating in water with a restoring force...
Apr14-14 11:34 AM
the_wolfman
1 144
Hello, PF! As I was reading my P-Chem textbook, I noticed most thermodynamic equations involve partial derivatives,...
Apr13-14 08:18 PM
Mark44
3 174
I know that the standard definition for a slope field is ##\frac{dy}{dx} = f(x, y)##, but and if the equation given is...
Apr13-14 04:08 PM
HallsofIvy
1 110
f(x,y) = ln(9 - x2 - y2) Domain I got: (x, y) in R2 such that x2 + y2 < 9 How do I find the range from the...
Apr12-14 12:09 PM
JC3187
6 164
Show that the explicit Runge-Kutta scheme \begin{equation} \frac {y_{n+1} -y_{n}}{h}= \frac{1}{2} \end{equation}...
Apr10-14 07:21 PM
rickyflair
2 168
If a system of first-order ODEs like ##\frac{d\vec{r}}{dt}=A\vec{r}## have as solution ##\vec{r} = C_1 \exp(\lambda_1...
Apr10-14 02:58 PM
Jhenrique
9 313
Hi All, I am taking Dynamic Systems and Controls this semester for Mechanical Engineering. We are solving non...
Apr9-14 12:40 AM
MisterX
1 202
You can give me a good examples where ##\frac{\partial}{\partial x}## is different to ##\frac{d}{dx}## ?
Apr8-14 09:12 AM
Jhenrique
2 200
Hello I am having some trouble understanding what the difference is between the reference solution and the "true"...
Apr7-14 07:36 AM
jjr
2 244
Hello guys, suppose we have an eigenvalue problem \left\{ \begin{array}{ll} u'' + λu = 0, ...
Apr2-14 10:44 AM
AlephZero
6 324
I realized that a PDE of 2nd order can written like: A:Hf+\vec{b}\cdot\vec{\nabla}f+cf=0 \begin{bmatrix} a_{11} &...
Apr1-14 09:22 PM
Jhenrique
0 214
Hi, I am looking for a solution of \frac{\partial\phi}{\partial t} =...
Apr1-14 06:50 AM
soni
0 201
Which the difference between diff equations of kind: \frac{dy}{dx} = \exp(x) \frac{dy}{dx} = 1/x and diff equations...
Apr1-14 02:22 AM
Mark44
8 228
Hello, I have been trying to find an equation to represent the observed angular velocity of any object traveling in a...
Mar31-14 08:50 PM
bendloewen
3 235
Hello, I'm trying to analyze a system of elastically coupled oscillators, whose masses are all the same, using...
Mar31-14 10:51 AM
Runei
1 182
Hello, I am doing some physics and I end up with this PDE: \frac{\partial q(x,y,t)}{\partial t} = -(x^2 +...
Mar28-14 02:51 PM
kosovtsov
4 500
How do we solve a system of coupled differential equations written below? -\frac{d^2}{dr^2}\left( \begin{array}{c}...
Mar27-14 11:04 PM
Ravi Mohan
2 290
Given a implicit ODE like F(x, y(x), y'(x), y''(x)) = 0, why your explicit form is y''(x) = f(x, y(x), y'(x))? Why a...
Mar27-14 12:36 PM
micromass
4 242
If we have a constant coefficient second order homogeneous ODE, the way to solve this is to suppose a solution of the...
Mar27-14 08:13 AM
quasar987
4 230
hello pf! i am wondering if anyone here knows of a geometric, intuitive explanation for the laplace transform? if...
Mar26-14 05:34 PM
micromass
3 221
I would like to learn this. Can someone teach me? The things like δy2/δ2x and solving for x and y. :rolleyes:
Mar26-14 12:37 AM
z.js
10 466
I want to solve y''+y'+y=(sin(x))^2 and try to use y=Ae^{ix} but then when I square it I get A^2 e^{2ix} ...
Mar26-14 12:26 AM
lurflurf
1 208
Hi, I know the weak form of the Poisson problem \nabla^2 \phi = -f looks like \int \nabla \phi \cdot...
Mar25-14 01:12 PM
pasmith
1 224
It is very clear that the solution to the equation "dy/y-a*dx/x = 0" is y=C*x^a. However I cannot figure out the...
Mar24-14 05:27 PM
maajdl
5 227
Apparently it is a well-known fact that if G(x)=(G_{ij}(x_1,\ldots,x_n)) is a smooth nxn matrix-valued function such...
Mar20-14 03:04 PM
quasar987
0 360
px = t t = s^2 $$ I = \int_0^∞ e^{-s^2}ds$$ $$I*I = \int_0^∞ e^{-s^2}ds * \int_0^∞ e^{-u^2}du = \int_0^∞\int_0^∞...
Mar19-14 03:11 PM
HallsofIvy
2 329
Hi, this question came up in my midterm and I was hoping to know if this is the correct method or answer.
Mar18-14 04:18 PM
pasmith
5 387
Hello, I am learning about the general solution to higher order linear non-homogeneous differential equations. I know...
Mar17-14 11:59 PM
lurflurf
1 304
I am trying to work though an example on this topic in my book and have reached a point that I am not sure about. I...
Mar17-14 04:00 PM
jellicorse
2 287

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