Differential equation Definition and 1000 Threads

Homework Statement Show that f(x) = A exp(σx) + B exp(-σx) is a solution to the following differential equation: f''(x) = (σ^2)f(x) where A, B, and σ are constants. What if a boundary condition is included that f(-∞) = 0? Homework Equations differential equation: f''(x) =...

Given a matrix differential equation (system of equations?) of the form: \textbf{X}^{\prime}(t) = \textbf{AX}(t) (where X is a complex matrix, t is real scalar and A is always a square and normal real matrix) I am able to find (e.g. here) that a general solution for square \textbf{X} is...

Take for example a system \frac{dx_i}{dt}=(x_i,t,a,b,...) i-number of state equations. What would be the maximum number of parameters permitted for this system of non-linear differential equations? Is it finally determined by the solution space?Is there a criteria for number of...

Homework Statement Verify that the differential equation, {\frac{dy}{dx}} = 15 - {\frac{2y}{81+3x}} has the general solution y(x) = 3(81+3x) + C(81+3x)^{-2/3} 2. The attempt at a solution I've just learned about differential equations, so I'm probably missing something very...

Homework Statement dy/dx = (y^2 - 1)/ (x^2 - 1) with initial condition y(2) = 2 Why is y = 1 and/or y= -1 not solutions? Homework Equations The Attempt at a Solution I am actually able to solve this differential equation but when I separate the equation according to x and y...

Homework Statement The Second Order Differential Equation is: x''-u(b^2 + x^2)x'+x=0 Initial Conditions are: x(0)=1 x'(0)=0 It is to be numerically solved for 0<=t<=500. The specific numerical method to be used isn't specified, but it must be programmed into c. As a means to check the...

Plese give me silminer simple example or anther example on this case or explein the steps

I try to show, that equation \frac{-y}{ x^{2}+y ^{2} } + \frac{x}{ x^{2}+y ^{2}}y'=0 is not exact in \mathbb{R^{2}} \setminus \{(0,0)\}. It's obvious that I have to use the fact, that the set is not simply connected, but I don't know how to do it.

I have the following equation \frac{\partial}{\partial y}\left(y\frac{dm}{dx}+m\frac{dy}{dx}\right)-\frac{dm}{dx}=0 where m is a function of y (say m=f\left(y\right)) and y is a function of x (say y=g\left(x\right)). Are there any conditions under which \frac{dm}{dx} becomes identically...

In Rayleigh's DE : http://www.wolframalpha.com/input/?i=rayleigh+differential+equation What does mu stand for?

I have the following equation \frac{\partial}{\partial y}\left(m\frac{dy}{dx}\right)=0 where y is a function of x and m is a function of y. If I integrate this equation first with respect to y should I get a function of x as the constant of integration (say C\left(x\right)) or it is just...

Homework Statement Find a differential equation with its only (complex-valued) solution being y=0Homework Equations The Attempt at a Solution I believe that there is no DE having only y=0 as its solution, but frankly I am not sure if this is the case. I would like to know whether or not this is...

What is the solution of the follwoing differential equation \frac{\partial^{2}y}{\partial x^{2}}-ay^{-1}\frac{dy}{dx}=0 where a is a constant.

What is the logic behind equating differential equations to zero? For example the equation y''-5y'+6y=0 Because it can just as easily be written y''-5y'=-6y I am interested in the meaning of why if we sum y''+(-5y')+6y equals zero. What is the relationship of its second derivative, first...

This may be vague, so I apologize. I am interested in applied mathematics, so my question is about the process a scientist or engineer uses to determine what differential equation to use for a non-linear process. I am not familiar enough with describing non-linear processes to be able to...

I was busy doodling and basically ended up constructing this differential equation: p'(t)=c(t)p(t)-c(t-T)p(t-T) Obviously I've dealt with eq's like p'(t)=c(t)p(t) but I'm getting stuck because of the second term. Does this differential equation even have a closed form? Thanks.

Homework Statement Given the initial value problem: \frac{(u)}{(1-e^-(2x))}u_{x}+ \frac{\sqrt{t}}{u}u_{t}=1, with x, t, u > 0 Subject to condition u(x,1)=e^{-x} Homework Equations a) Classify given partial differential equation. b) Write the characteristic equations. By...

What is the general solution to the differential equation describing a mass-spring-damper? t=time x= extension of spring M=Mass K=Spring Constant C=Damping Constant g= acceleration due to gravity Spring has 0 length under 0 tension Spring has 0 extension at t = 0 If the Force...

Homework Statement The trajectory of an arrow in space obeys the following system of equations: \dot{x} = y+(x^2+y^2-3)^2 (x^3-x+xy^2) \dot{y} = y+(x^2+y^2-3)^2 (y^3-y+x^2y) 1. Questions a) Derive an ODE for the radial coordiante r(t) = \sqrt[]{x^2(t)+y^2(t)} b) Show that the...

For example, if y=x^2, then the derivative of y is 2x. We write the derivative as either f'(x)=2x or dy/dx=2x. Well, the differential equation is also written as dy/dx=2x. So is there a difference between a differential equation and a derivative? !~Alshia~!

Homework Statement The Attempt at a Solution I don't think this is the correct answer because for some reason I have a constant mg term. Usually I get mgsinθ and from small angle approximations it becomes mgθ, but this time I am getting mgcosθ and from small angle approximations it...

Hello. I'm having a hard time solving this homework question, even though I know I shouldn't... but well. Here's the problem : -The K switch is closed for a long time, so as to be in a steady state. What's the electric charge of the capacitor ? Infer vs tension from this. Which...

I have a quick question. I have to write the differential equations in matrix form Eq1:= x1'(t) = -a1*x1(t) + vf Eq2:= x2'(t) = a1*x1(t) - a2*x2(t) is this correct :

Homework Statement A disk or radius b rotates about a rod in its center with a constant angular velocity, Ω. At the disk's edge A, a pin is attached allowing for a body to be attached an freely swing during the rotation. Determine the differential equation for the angle β between the attached...

Homework Statement Oil is released from a submerged source at a constant flow of rate of Q=(0.1 m3)/s. Density of oil (p=870 kg/m3) is less than that of water and since oil is only sparingly soluble in water a slick will form on the water surface. Once its formed it will have a tendency to...

This is a case where an object is coupled to a spring, laying on a table. The object is moving, friction less, horizontally on the table. We assume the object is moving in an outer forice field which acts in the same direction as the object's motion. The motion is modeled by y''(t) + y(t) =...

Q. Find SP of:\dddot{x} + \ddot{x} + \dot{x} = x^3 -2x^2 - 31x -28 x(t)=x And determine of the solutions as stable or unstable. OK, not seen one like this before. I've done it with 2nd order derivatives and wondered if it was the same. by setting the derivatives to zero and solving the RHS...

Homework Statement given: dt=-\frac{1}{2}\sqrt{\frac{l}{g}}\frac{d\theta}{\sqrt{sin^2(\alpha/2)-sin^2(\theta/2)}} make the change of variables sin(\theta/2)=sin(\alpha/2)sin(\phi) to show that: dt=-\sqrt{\frac{l}{g}}\frac{d\phi}{\sqrt{1-k^2sin^2(\phi)}} where k=sin(\alpha/2) Homework...

I'm trying to find the gen. solution to the equation y''''-8y'=0 I found the characteristic polynomial by plugging in ert as a solution to y. I got, r^4-8r=0 I simplified to get r*(r^3-8) Thus one root is 0, for the other 3 i must find the cubed root of 8. I know the answer is...

Any idea on how they got from first line to second? They just ate the (-1/9)e^(3x)...(picture is attached)

Homework Statement y" + y = 4δ(t-2π); y(0)=1, y'(0)=0 Homework Equations L[f(t-a) U(t-a)] = e^{-as} L[f(t)] L[δ(t-c)] = e^{-cs} The Attempt at a Solution My answer is: cos(t) + 4U(t-2π)sin(t-2π). When I used Wolframalpha it gave me 4sin(t)U(t-2π) + cos(t)

Homework Statement Find a solution for: u'(t)=c*u(t)^2-c*(a+b)*u(t)+c*a*b The Attempt at a Solution I've found the solution for the homogeneous equation: u_0(t)=(\frac{1}{a+b}+d*e^{c(a+b)t)})^{-1} Where c is a random constant. Now I've tried the solution u(t)=x(t)*u_0(t), when I fill...

Homework Statement Use the power series to solve the following differential equations, state the first four terms of the two independent solutions. 3xy'' + y' - y = 0 Homework Equations The power series. The Attempt at a Solution How do I get two independent solutions out of this? All...

What is the function corresponding to this ODE: http://home.arcor.de/luag/math/dgl.jpg In complex notation it obviously shows up like this: a * z''(t) + b * |z'(t)| * z'(t) + c = 0; The numerical solution shows a graph resembling to a cycloid. Thanks for any help! Tom

So, I have a differential equation with growth problem. It is a dm/dt function and I need to get it to dD/dt, change in diameter with time. here is the original functon, dm/dt= (pi/4)(D)^2* (V(D))*(LWC)*E E=1 LWC = 2 V(D) = 343D^0.6 m/s it starts from a diameter of 1mm and grows to...

I am having a problem finding the solution for this eq: y''(x)+(2/x)y'(x)+(w^2)y(x)=0 I couldn't find examples in the textbook that goes on a similar line, and have been searching the internet as well, but no use. I am thinking of using substitution v=y' but not sure how to do that in the...

Hey all, I'm stuck on a dynamic systems question, it's attached as a jpeg I started off by writing nodal equations for each node: Node 1: 1/R1(ei-eA)=C1D(eA-eo)+1/R2(eA-eB) Node 2:1/R2(eA-eB)=C2D(eB) I know that I have to isolate for ei and eo but I'm really confused with...

How to covert this differential equation into a system of one order ODE? (require covert the equation into a system of 1st-order equations and solve by using ode23 in matlab) x^2*y''-2*x*y'+2*y = 0; y(1) = 4; y'(1)=0; solve for y(x) I tried to convert it get X' = AX in which X...

How to covert this differential equation into a system of one order ODE? x^2*y''-2*x*y'+2*y = 0; y(1) = 4; y'(1)=0; solve for y(x) I tried to convert it get X' = AX in which X = [y, z]' A = [0, 1; 2/x^2, 2/x]; But x exists in A, which cannot solve by dsolve in Matlab.

Homework Statement y''+0.1y'+y=1+2\sum_{k=1}^{n}(-1)^{k}u_{k\pi}(t) and quiescent initial conditions. Homework Equations None. The Attempt at a Solution (s^{2}+0.1s+1)Y(s)=\mathcal{L}\{1\}+2\sum_{k=1}^{n}(-1)^{k}\mathcal{L}\big\{ u_{k\pi}(t)\big\} I'm not sure if this step was...

use method of reduction of order to find second solution: t2y''-4ty+6y = 0 , y1(t)= t2 Attempt: So I've done all the steps, up to the substitution, but I'm having problems with what appears to be a simple linear equation but I can't solve it: Any ways, with w = v' I arrive at...

μ^{2}\frac{d^{2}u}{dx^{2}}+ae^{u}=0 Boundary conditions: u(-L)=u(L)=u_{0} Solve by multiplying by \frac{du}{dx} and integrating in x I know you have to use substitution, but I keep going in circles.

Hiya. I have to solve this bad boy under the assumptions that f, f' and f'' tend to 0 as |x| tends to infinity: 1/2(f')^2 = f^3 + (c/2)f^2 + af + b where a,b,c are constants. My thoughts are use Fourier Transforms to use the assumptions given, but not sure how to do them on these terms...

Homework Statement I am trying to find the parametric equation that describes the following second order differential equation: Homework Equations m\frac{d^2y}{dt^2}=-mg - k\frac{dy}{dt} Where m, g, and k are all constants. The Attempt at a Solution I substituted u=\frac{dy}{dt} to reduce...

Homework Statement Use L'Hospitals rule to show that lim x->0 x^a ln(x) = 0 I don't know how to solve this. I guess the first thing to do is to transform it in some way so that one can use L'Hospitals rule, but I don't know how. Thank you! EDIT: a>0 It's not a differential equation as...

I'm not sure how to solve this: du/dt = 3 \frac{d^{2}u}{dx^{2}} These are the conditions: u(0,t)= -1 u(pi,t)= 1 u(x,0) = -cos 7x Suggestion: I should use steady state solution to get a homogeneous initial condition. Starting with separtion of variables u(x,t) = G(x)H(t) And...

Homework Statement Find an integrating factor for the first order linear differential equation \frac{dy}{dx} - \frac{y}{x} = xe^{2x} and hence find its general solution Homework Equations The Attempt at a Solution I found the integrating factor which is e^{-lnx} = x^{-1} and...

Mod note: HTML size = ... tags are not needed. You can make things look just fine using [ tex ] tags instead of [ itex ] tags. So, I was doing some stuff, messing around when I thought of something. What if I took a random physics formula and integrated it into the original function? Then I was...

How to solve \( (x+1) y'' - (2x+5) y' + 2y = (x+1) e^x\) can we assume \(y_1 = (Ax+B) e^x \), then \(y_2= vy_1​\) Is this right? then solve for A and B Finally \( y = c_1 y_1 + c_2 y_2\)

Consider a circle of radius 'a' and centre (h,b) then the equation of the circle is given by (x-h)2 + (y-b)2 = a2 I expressed this in terms of differential equations which is - a= {[1+(dy/dx)2]3/2}/{d2y/dx2} According to my book - this equation indicates that 'a' is a...