Differential equation Definition and 1000 Threads

Solving differential with a step impulse. Hi, I have problem I know I should be able to do but I've been stuck on it for a while. Just looking to be pointed in the right direction. (dq^2/d^2t) + 2*ζ*ω*dq/dt + (ω^2)*q = u(t)/L Where u(t) is a step impulse, q is the charge through an...

Hi MHB. I'm having yet another doubt regarding differential equations. Can someone please help me out? Thanks. Consider the following differential equation: {y}''+{y}'= x^{2} I have found the homogeneous solution to be: y_{H}=c_{1} + c_{2}e^{-x} But when finding the particular solution...

Homework Statement A car starts from rest.When it is at a distance s from its starting point,its speed is v and it acceleration is a = (25v + v^3). Show that dv = (25 + v^2)ds and find its speed when s = 0.01 2. The attempt at a solution a = v(dv/ds) = (25v + v^3) divide both sides by v...

Homework Statement Okay, I am trying to solve this Anharmonic Oscillator equation. Now I am given with the potential U=(1/2)x^2-(1/4)x^4 and Kinetic energy T=(1/2)x' ^2 So the Lagrangian becomes \mathcal L=T-U Now I have taken all the k's and m to be 1 Homework Equations...

Hi MHB. Can someone help me with this one please? I don't understand what the question is really saying...in particular part (c). I tried to set up dD/dt = k - D^1/2 but it doesn't seem correct. Thanks.

Can someone please help me with this one? I have found the equilibrium solutions,but I'm not sure what to do next. Consider dx/dt = x^3 - 4x Given a solution x(t) which satisfies the condition x(0) = 1, determine the limit(t -> infinity) of x(t). Thanks!

Homework Statement Solve d^2x/dt^2 = (3x^3)/2 when dx/dt = -8 and x = 4 when t = 0 2. The attempt at a solution v = dx/dt dv/dx = d^2/dx^2 d^2x/dt^2 = v(dv/dx) = (3x^3)/2 v dv = (3x^3)/2 dx integrating and using limits and you get : v^2/2 -32 = (3x^4)/8 - 96 ...

I need to solve the following system of equations for n=0,1,2 subject to the given initial and boundary conditions. Is it possible to solve the system numerically. If yes, please give me some idea which scheme I should use for better accuracy and how should I proceed. The coupled boundary...

For polar coordinates, ##u(x,y)=u(r,\theta)##. Using Chain Rule: \frac{\partial u}{\partial x}=\frac{\partial u}{\partial r}\frac{\partial r}{\partial x}+\frac{\partial u}{\partial \theta}\frac{\partial \theta}{\partial x} The book gave \frac{\partial ^2 u}{\partial x^2}=\frac{\partial...

Homework Statement using the method of separation of variables, solve ∂u/∂x=4∂u/∂y, where u=3e^-y - e^-5y when x=0. Homework Equations The Attempt at a Solution let u(x,y)=X(x)Y(y) =XY.

Homework Statement Solve (d^2x)/(dt^2) = 2x(9 + x^2) given that dx/dt = 9 when x = 0 and x = 3 when t = 0 Homework Equations The Attempt at a Solution v = dx/dt ...... dv/dx = d^2x/dt^2 dv/dx = v(dv/dx) v(dv/dx) = 18x +2x^3 integrating and evaluating using...

Hi, I'm somewhat new here, only posted a few times, and would like some help from you guys here if possible I'm stuck with a problem on the topic mentioned. x'=Ax A is a 2*2 matrix A = [-5 1] [-1 -3] Now I managed to find the eigenvalues which is -4, repeated twice (multiplicity 2) And the...

Homework Statement I have this physics mathematical problem : (see link in comment) EI(∂4u)/(∂x4) =f ......(1) The boundary conditions are: ∂2u/∂x2 =0 and EI ∂3u/∂x3 =±F where E is Young’s modulus, I is second moment of area, f is force per unit length...

Hi, The definition (see attachment) says that f(x) is a solution to the differential equation if it satisfies the equation for every x in the interval. Assuming that I have a differential equation that I want to solve and the D.E. has an interval I_1, and I've come up a solution with...

Homework Statement Right so I had a standard systems of diff eqs involving repeated eigenvalues. When I find the last vector I have the equation \begin{pmatrix} 1 & 1\\ -1 & -1 \end{pmatrix} \begin{pmatrix} u_1\\ u_1 \end{pmatrix} = \begin{pmatrix} 1\\ -1 \end{pmatrix}The Attempt at a...

\sqrt{1-y^2}dx - \sqrt{1-x^2}dy=0, y(0)=\frac{\sqrt{3}}{2} rewriting the equation gives \frac{1}{\sqrt{1-x^2}}dx = \frac{1}{\sqrt{1-y^2}}dy Isn't this the integral for \sin^{-1}(x) & \sin^{-1}(y)? The back of book has y=1/2x+\frac{\sqrt{3}}{2}\sqrt{1-x^2}

Homework Statement Find the general solution: y'' - y' - 2y = -2t + 4t^2 Homework Equations The Attempt at a Solution r_1 = 2, r_2 = (-1) Set Y(t) = At^2 + B^t + C Y' = 2At + B Y'' = 2A 2A - 2At + B - 2At^2 + Bt + C = -2t + 4t^2 -2At^2 + (B-2A)t + 2A + B + C = -2t...

Solve the given differential equation by separation of variables y\ln{x}\frac{dx}{dy}=(\frac{y+1}{x})^2 I got it down to \ln{x}x^3-\frac{x^3}{3}=y^3+3y+y^2 At this point I had no idea how to solve having y^3 y^2 and y terms so I did what any good student would do and checked the back of the...

Hello MHB, Solve the following system of linear differential equation f'=f-g g'=f+g with bounded limit f(0)=0, g(0)=1 could anyone check if My answer is correct? Just to make sure I understand correctly! ps we get \lambda=1-i and \lambda=1+i Regards, |\pi\rangle

Hello MHB, solve this system of linear differential equation f'=f-g-h g'=-f+g-h h'=-f+g+h with boundary conditions f(0)=1, g(0)=2 and h(0)=0 we get that \lambda=1 and \lambda=0 now for eigenvector or we can call it basis for eigenvector \lambda=0 i get Is that correct? Regards, |\pi\rangle

Hello, can you guys help me please with this differential equation from Demidovitch book, is to find the solution transforming to polar coordinates :

I need to prove that the solution of this differential equation: dx/dt = -x3 + 2*x + sin3(2*pi*t) - 2*sin(2*pi*t) + 2*pi*sin(2*pi*t) has the solution: ψ(t,0,0) = sin(2*pi*t) I know that I need to get all of the x's on one side and the t's on the other then integrate, but I can't...

Homework Statement Suppose that a fourth order differential equation has a solution y=-9e^(3x)xcos(x). a. Find such differential equation, assuming that it is homogeneous and has constant coefficients. b. Find the general solution to this differential equation. x is the independent...

I am trying to write out a differential equation for the Wien bridge oscillator circuit. I have attached a picture of the circuit. I am considering ideal conditions. I am trying to solve for the output voltage but I need help setting up the differential equation.

Homework Statement Problem 5 on the attached Sheet here Homework Equations We studied the Power Series Method and how to calculate a linearly independent solution if one solution is already known. So we need to find one solution (probably) using the power series method and then using...

Problem: Newton's 2nd Law for rotational motion states that the product of the moment of Inertia, I, and the angular acceleration alpha(t) is equal to the net Torque acting on a rotating body. Consider a wheel that is being turned by a motor that exerts a constant torque T. Friction provides...

Homework Statement Find the general solution to the following differential equation. dy/dx = 2x( (y^2) + 1) Homework Equations The Attempt at a Solution I got all x terms on one side and all y terms on the otherside 2x dx = 1/( (y^2) + 1`)dy integrate x^2 + c =...

Homework Statement dx/dt=x+y dy/dt=-y+8x Solve this system useing Eulers method or by elimination method. Homework Equations Eulers method I know that in general I should look for solution in form y=const*exp[kx] z=const2*exp[kx] But in my case I am not sure if i can write...

Homework Statement Solve y' = (y^3)(t^2) for the initial condition y(0)=0 and state in which interval in 't' this solution exists. The Attempt at a Solution First I divided both sides by y^3 and then subtracted t^2 from each as well, -t^2 + y'(y^-3) = 0 then solved, (-t^3)/3 +...

If we have \frac{1}{X(x)} \frac{d^2 X}{dx^2}=-κ^2, the literature is saying that the solution must be: e^(±iκx), but am always getting e^(±k^2x). Isn't the approach is to decently integrate twice and then raise the ln by the exponential? Where am I going wrong? Thanks

Homework Statement f(x,y)= 3x5y2 - 30x3y2 + 60xy2 +150 How do I find the critical points where this equation equals zero? Homework Equations None? The Attempt at a Solution I found the partial derivatives, but I'm stuck now and don't know where to go from here. dx = 15x4y2...

Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (x_0, y_0) in the region. x \frac{dy}{dx} = y What does an xy-plane have to do with anything? I looked up the definition of unique solutions and here it...

Make up a differential equation that does not possesses any real solutions. step 1)consider the definition of solution Any function \phi defined on an interval I and possessing at least n derivatives that are continuous on I which when substituted into an nth-order ordinary differential...

Verify the indicated function y=phi(x) is an explicit solution of the given equation. Consider the phi function as a solution of the differential equation and give at lease one interval I of definition. (y-x)y'=y-x+8 where y=x+4\sqrt{x+2} So the derivative is y'=1+\frac{2}{\sqrt{x+2}} and the...

Homework Statement It's been a long time since I've done DE's and now I'm stuck with a monster of this form: y'(t) = a*g'(t) + b*g(t) + c*y(t) where g(t) is a known function and a, b and c are constants. What kind of DE is this, and how can I solve for y(t) -- or better yet, what...

Homework Statement What are the bifurcation values for the equation: dy/dt = y^3 +ay^2 Homework Equations The Attempt at a Solution Equilibrium solutions: y^3 + ay^2 = 0 ==> y^2 (y + a) = 0 ==> y = 0 (double root), or y = -a. a = 0 is the sole bifurcation point, since...

Homework Statement Using Euler's Method: a) Find the approximate values of the solution of the given initial value problem at t = 0.1, 0.2, 0.3, and 0.4 using the Euler method with h= 0.1 b) Repeat part (a) with h = 0.05. I am doing part (b). The function is y' = 0.5 - t + 2y...

Hello I seek solutions of differential equation x3y′′(x)+(ax3+bx2+cx+d)y(x)=0 thank you

y'''-5y''+6y'=8+2sinx If I let w=y', would I be able to solve this differential equation? I'm currently stuck and I just want to know if making this substitution is why I am stuck.

I cannot figure out where I am going wrong. My answer and the textbook answer are different by a negative sign. Can someone review my work and tell me what I am doing wrong?

Hi guys! I am really stuck at quite a complicated (from my point of view) differential equation. I would really appreciate any hints or suggestions on how to tackle and solve it if it is possible, thanks...

Homework Statement Solve the separable differential equation for u du/dt=e^(5u+2t) Use the following initial condition: u(0)=13 The Attempt at a Solution Honestly I didn't get very far on this one. I took the natural log of both sides, ln du/dt = 5u+2t And now I am stuck. Should I divide...

1. Find a differential equation with the solution y(x) = (x + C)3 The answer cannot contain C) 2. There are no relevant equations. 3. I'm not entirely sure how to do this; I understand that a differential equation has multiple solutions, but for some reason I'm lost on how to find...

how do i find the yk value?? the k, tk and mk values makes sense to me Problem #1: http://imageshack.us/photo/my-images/14/fe0x.jpg/ Solution manual: http://imageshack.us/photo/my-images/5/hu55.jpg/

Homework Statement y = c1e3xcos(2x)+c2e3xsin(2x)+c3+c4x Homework Equations Differential Equations. The Attempt at a Solution I am having trouble what the roots are for the c3, and c4 parts. I know they are a repeated root, but is it just k= 0? It seems like it would work, but I...

Homework Statement y = c1e3x+c2xe3x+c3e2xsin(x)+c4e2xcos(x) Homework Equations Differential Equations. The Attempt at a Solution I have the roots of k=3, k=3, k=2+i, k=2-i. Now I am just stuck on how to put the roots together to get the original equation. I am just stuck on the complex...

Hi I am working on a problem that ends up having the natural log of a negative e which I'm confused on how to find the explicit solution. The Problem: Find an explicit solution with C. y'-e^{-y}cos(x)=0 My Conclusion: First of all, I'm confused how I should solve this explicitly if I'm...

Homework Statement Find the input/output differential equation for the LRC circuit in the given figure. The figure is shown in the attachment. Homework Equations V(t) = Ri(t) For inductor, v(t) = Ldi(t)/dt I(t) = 1/L∫v(λ)dλ For capacitor, dv(t)/dt = i(t)/C v(t) = 1/C∫i(λ)dλ...

I have the differential equation \frac{dM}{dt}=4\pi \rho(r,t)r(t)^2\frac{dr}{dt} which is the first term from M(t)=4\pi\int_0^{r(t)}C(r,t)r(t)^2dr This describes the change in mass (M) of a sphere from a change in radius (r) given a density (rho) that depends on radius and time (t). My...

The mass of a sphere with density as a function of radius is M=4\pi \int_0^r\rho(r) r^2dr Lets say the radius increases and decreases as a function of time t. So: M(t)=4\pi \int_{0}^{r(t)}\rho (r) r(t)^2dr I want to know the basic equation describing the mass added or removed...