Differential equation Definition and 1000 Threads

Homework Statement A rocket through interstellar dust, no gravity. Solve for v with respect to mass. k is a constant. Drag = -bv Homework Equations [/B] The Attempt at a Solution To start: It should become a separable differential equation, but I am having a lot of trouble solving it...

Amazed by the closeness of equations for orbital angular momentum L and spin angular momentum S, I can't help asking is associated Legendre differential equation involved in solving spin function? I only heard that spin naturally comes from treatment of quantum mechanics with relativity theory...

Homework Statement If y=y(t) is the solution of the initial value problem { y'+(2t+1)y=2cos(t) y(0)=2 then y''(0)=? it is a multiple choice practice problem with choices y''(0)=2 y''(0)=-2 y''(0)=4 y''(0)=0 y''(0)=-4Homework EquationsThe Attempt at a Solution Im really not sure how to go...

Homework Statement Find the general solution: y'-3y=(y^2) Homework EquationsThe Attempt at a Solution divide both sides by y^2 y'(y^-2) -3(y^-1) = 1 we know v=y^(n-1) v=y^-1 v'=d/dx(y^-1) v'=-(y^-2) y' plug it back into y'(y^-2) -3(y^-1) = 1 -v'-3v=1 this is where I think I am making a...

Can you prove a differential equation has no analytical solution? Teach me ,please! Thank you a lot!

I want to solve a differential equation of the form d/dt (R) = B(t) where R and B are two complex matrices, with time dependent functions as their coefficients. I want to solve these 3x3 differential equations (ones on the diagonal are actually coupled) and to obtain a matrix form for R. So...

Homework Statement In the limit as t→∞, the solution approaches x(t) =K \sin[ω(t − t_0)] where K and t0 depend on ω. A>0 and ω≥0. Show that K(ω) = \frac{A}{\sqrt{ω^4 + 2ω^2 + 1}} . Homework Equations Here is the differential equation...

Homework Statement (\partial_t - A\nabla^2 + B)f(x) = \eta(x, t) So I have a homogeneous linear differential equation except for an added noise term ##\eta(t) ##. The noise is uncorrelated between times and has a Gaussian distribution with zero mean. That is we have Gaussian white noise...

So I'm currently taking electricity and magnetism and I'm expected to know how to perform a separation of variables on laplace equation in 2 dimensions.I have taken Zero differntial equations courses and I literally have no freaking idea what's going on. The book I use doesn't spend any time...

Homework Statement In the circuit in the following figure, the resistor is adjusted for critical damping. The initial capacitor voltage is 15 V, and the initial inductor current is 6 mA and R=1250 ohms Find vC(t) for t≥0. Express your answer in terms of t, where t is in milliseconds...

Hi. How can i solve below equation with ndsolver ? dp/dt = a * d^2p/dx^2 * cos^2 (theta) + b d^2p/dt^2 + c d^2p /d(theta)^2 where a , b, c are constant. d^2p/dx^2 is second derivative with respect to x. theta is angle.

Homework Statement This is actually an electromagnetism problem but all the physics is done, I just don't remember how to solve the PDE: \frac{d^2V}{dr^2}=-\frac{2}{r}\frac{dV}{dr} The d's should be del's, just don't know how to do that... Homework Equations Not sure. The Attempt at a...

In the attachment I have used the derivation of the wave equation with a slight modification to derive the diff equation that when solved gives the time independent schrødinger equation. Since I have dome this myself I am worried that this might be totally wrong or a bit wrong. Could someone...

I am would like to solve this differential equation: Where http://ieeexplore.ieee.org.ezproxy.uniandes.edu.co:8080/ielx5/8/6493417/6409989/html/img/6409989-eqdisp-3-small.png Could you give me some practical ideas about the required software and methodology? Thank you very much

Homework Statement Find the differential equation that Q(t) satisfies. 2. Relevent equations Kirchoffs loop law and voltage across a capacitor, resistor and inductor. The Attempt at a Solution [/B] So I'm thinking, by Kirchoffs voltage rule, that the sum of the voltages in this circuit...

Homework Statement The problem is Solve the following differential equation: dy/dx = 6*x*y/(3-x^2) Homework Equations Okay so I know the first step is integrating both sides and separating the variables The Attempt at a Solution So separating the variables and integrating I get integral of...

Homework Statement y'' + 4y' + 4y = 0 ---- y(0) = 1, y'(0) = 5 Find the exact solution of the differential equation. Use the exact solution and Euler's Method to compute Euler's Approximation for time t = 0 to t = 5 using a step h=0.05. Plot Euler's & Exact vs. t and plot Error vs. t. Then...

Homework Statement 2y * y'(t) = 3t^2 such that y(0) = 9 Homework Equations g(y)y'(t) = h(t) The Attempt at a Solution So I have done many of these seperable ones in homework that did not require a parameter so now I got lost. This is what I did;[/B] Integral of 2y dy = integral of 3t^2...

A ball of mass 'm' is inside of a tube that rotates in a horizontal plane around the vertical axis (Drawing a circunference). Attached to the ball (inside of the tube) there is a massless, inextensible rope that goes to the midpoint of the circle described by the rotating tube. The other end of...

So, I should prove that: - \frac{\partial H}{\partial q_i} = \dot{p_i} And it is shown that: - \frac{\partial H}{\partial q_i} = - p_j \frac{\partial \dot{q_j}}{\partial q_i} + \frac{\partial \dot{q_j}}{\partial q_i} \frac{\partial L}{\partial \dot{q_j}} + \frac{\partial L}{\partial q_i} =...

Is the derivative of a function a differential equation? I guess it would be because it involves a derivative, right? Would the solution to the equation just be the original function? Is solving a differential equation just another way of integrating? Like with finding solutions of separable...

from the attached file I get something like the answer as y(x) = e^(e^2x(x/3*(sin(3x)+1/9cos(3x)+c) Im not sure if this is right can you have an answer exponetial of an exponential??

Homework Statement Consider the differential equation y'=x-y^2. Find maxima, minima and critical points; show that for every solution f=f(t) exists T\geq 0 such that f(t)< \sqrt{T}\;\forall t > T Homework Equations The Riccati equation: y'=a(x)y^2+b(x)y+c(x) The Bernoulli equation...

Homework Statement By truncating the differential equation below at n=12, derive the form of the solution, obtaining expressions for all the ancoefficients in terms of the parameter \lambda .Homework Equations The ODE is: \frac{\mathrm{d^2}\phi }{\mathrm{d} x^2} = \frac{\phi^{3/2}}{x^{1/2}}...

Hi, I need help solving this ODE. I know the answer is a Bessel function but I need help on the process of getting there. Initial conditions y(0)=1 and y'(0)=0 xy''+y'+xy=0 I have made it this far... ${x}^{2}*\sum_{n=0}^{inf} [n(n+1)*{C}_{n+2}+(n+1)*{C}_{n+1}+{C}_{n}]*{x}^{n}=0$

Homework Statement Solve the differential equation: \frac{dy}{dx} = x + y Homework Equations Integrating factor equationThe Attempt at a Solution Ok, I am aware that in order to solve this equation, I need to make a substitution: v = x + y However, at this point I am unsure about what to...

How do I go about solving a differential equation of the form \partial_{x}F_{x}(x,y) + \partial_{y}F_{y}(x,y) = g(x,y) Where g(x,y) is a known function and I wish to solve for F. I thought i could apply the method of characteristics but the characteristic equation is dependent on coefficients...

Hi, I need help solving this ode, when I try to solve it I end up with a big crazy answer and I believe it should be simpler. (dy/dx)^2=((ay^4)/2)-(a+1)y^2+1 y(0)=0, y'(0)=1 and a is within [0,1]

Solve the 2nd order nonlinear differential equation, with initial conditions y(0)=0 and y'(0)=1 y''=2ay^3-(a+1)y with a within [0,1] I am pretty much lost on how to go about solving this. It would be greatly appreciated if someone could point me in the right direction on this. Thanks!

In class we discussed RLC circuits in series. My homework problem, however, has me analyzing an RLC circuit in series. a) Write the differential equation that describes the voltage with respect to time. b) Find the natural frequency of oscillation and the damping constant of the circuit...

Homework Statement Mass , r, of a round object grows in proportions with its SA. The density of the object is constant. Find the differential equation for the change in 'r' of the object over time. Arbitrary constants can be combined but final answer must depend on only r and constants...

For each epsilon greater than 0, show that the differential equation x'=x^2-1-cos(t)-epsilon has at least one periodic solution with 0 less than x(t) less than or equal to (2+epsilon)^1/2

Homework Statement I want to solve number 13. I have my work on the attached file. Homework Equations The Attempt at a Solution I've tried to solve the system by elimination and substitution. I keep failing again and again

Homework Statement y'sin(2t) = 2(y+cos(t)) y(\frac{∏}{4}) = 0 Homework Equations \frac{dy}{dx} + p(x)y = q(x) y = \frac{\int u(x) q(x) dx + C}{u(x)} where u(x) = exp(\int p(x)dx) The Attempt at a Solution I've set the equation in the form above, simplified the RHS and solved for...

Hi everyone, I need some help to solve this differential equation. The question states "Use the perturbation or multiple scale method to find the third-order approximate solution for the following system: diff(x(t), t, t)+w^2*x(t)*(1+epsilon*x(t)^2) = 0 " Currently, I am still...

Hello. I need some help solving a differential equation. I think where I'm going wrong is integrating one side via partial fractions, but I'm not quite sure where my mistake is. Using Wolfram, I found the correct answer, which is below. Thanks. Homework Statement Solve the following initial...

Hi all , I would like to solve the following partial differential equation. (∂α/∂t)=G[sub(α)] *(a'-a) I attached the equation and solution here as an image. I don't know how it was derived. I hope someone can help me

My textbook defines differential equation as Could someone explain what is meant by the part in parenthesis "dependent variables"? I don't see the difference.

I was wondering if there is a way to get specific numerical values for the following differential equation: f'(x)+ \frac{1}{x-20}\cdot f(x)=\frac{1}{x-20}\cdot g(x) I have numerical values for g(x) for about 10 different x values. I need to find f(x) numerically for those same values...

I want to model a Differential Equation for a projectile motion under 2 forces (gravity and wind) So, what I have now is an algorithm that simulate the parametric motion (2d) of the project under those 2 forces (given a P position of the projectile with velocity V under a vector of forces F (or...

Homework Statement Find the solution to ## \frac{dy}{dx} = yLn(y + 1) ## Homework Equations ## \frac{dy}{dx} = yLn(y + 1) ## The Attempt at a Solution ## \frac{dy}{dx} = yLn(y + 1)## ## \frac{dy}{yLn(y + 1)} = dx ## but then i can't integrate, any help?

Homework Statement Find the power series solution of the differential equation y''-\frac{2}{(1-x)^2}y=0 around the point ##x=0##. Homework Equations y=\sum_{n=0}^\infty{}c_nx^n y'=\sum_{n=0}^\infty{}c_{n+1}(n+1)x^n y''=\sum_{n=0}^\infty{}c_{n+2}(n+2)(n+1)x^n The Attempt...

Homework Statement okey, so i got stuck at another step in the way of solving de's.I've been studying DE of this form: y' + P(x)y = Q(x) Homework Equations The Attempt at a Solution So, first we solve y' + P(x)y=0 for y. \frac{dy}{y} = -P(x)dx , we integrate this and get...

Homework Statement I'm starting college this autumn(physics) and I started learning some calculus on my own, basic stuff like first order differential equation and so on.Recently i stumbled on something that i don t understand.I was reading the course and re-solving the given examples for...

My book says: "Differential equations of the form $$\frac{\mathrm{d} y}{\mathrm{d} x}=f(x,y)$$, where $$f(x,y)$$ is homogenous function (function is homogenous if $$f(tx,ty)=t^k f(x,y)$$) can be written in form $$\frac{\mathrm{d} y}{\mathrm{d} x}=F(\frac{y}{x})$$ and transformed to differential...

I am new to SDE, and especially Ito's Lemma. I have a question that I simply cannot answer. It attached. Can someone please help?

I have this equation: dy/dx = 1-y^2, so then dy/(1-y^2) = dx, so ∫dy/(1-y^2) = dx ---> ∫(A/(1+y) + B/(1-y))dy = x + C. I rewrite it again: (A - Ay + B + By)/(1+y)(1-y) = 1/(1+y)(1-y) so I get A+B = 1, and B-A = 0, so B = A, and therefore 2A = 1. so A & B = 1/2. So 1/2∫(dy/(1+y) +...

Definition/Summary An nth-order linear ordinary differential equation (ODE) is a differential equation of the form \sum_{i=0}^n a_i(x)y^{(i)}(x)\ =\ b(x) where y^{(i)}(x) denotes the ith derivative of y with respect to x. The difference between any two solutions is a solution of the...

Homework Statement a) Write (x21)y'+2xy as the derivative of a product b) Solve (x21)y'+2xy=e-x The Attempt at a Solution a) I use the product rule backwards and get ((x2+1)y)' b) I exploit what i just found out... (x21)y'+2xy=((x2+1)y)' and get... e-x=((x2+1)y)'...

My textbook says that: "A differential equation contains both the function and the derivative of the function" and at the same time claims that y'=3x2 is a differential equation. How can this be? The original function isn't part of the equation in this case?