Differential equation Definition and 1000 Threads

I am really confused where to start with this problem. I know about convolutions somewhat. We have done them a little. Where is a good place to begin with this problem?

Hi Everyone! I am really stuck at one differential equation: (p-y)^{2}y'(x)+(x-y)(x+y-2p)=0 where p<x<1; \ 0<y<p; \ p - parameter, 0<p<1 I have a suspicion that it does not have a solution, but is there a way to prove it mathematically in this case? I would appreciate any hints on...

Homework problem for nonlinear dynamics. Let us write xλ(t) for the solution of the initial value problem \dot{x} = f(x) & x(0) = λ where f is continuously differentiable on the whole line and f(0) = 0. a) Find the differential equation for \frac{∂x_{λ}}{∂λ}(t) I'm a little confused...

EDIT: Nevermind I see what I did wrong near the end. Homework Statement x'' + 4x = f(t) Where f(t) is 1 if t is between 0 and π, 0 if t > π. Initial conditions are x(0) = x'(0) = 0. Homework Equations Transform of a derivative: L(f^{(n)}(t)) = s^nF(s) - s^{n-1}f(0) -...-f^{n-1}(0)...

Homework Statement Solve the following differential equation. y'= {{2,-1},{3,-2}}y + {{1},{-1}}(e)^{x} If it's not clear, I made an image for it. http://i.imgur.com/lypTxqf.jpg Homework Equations y{g} = y{h} + y{p} The Attempt at a Solution So basically, I am looking for...

Hey everyone. Need some more pairs of eyes for this one: "For each positive integer ##n##, the Bessel Function ##J_n(x)## may be defined by: J_n(x) = \frac{x^n}{1\cdot3\cdot5\cdots(2n-1)\pi}\int^1_{-1}(1 - t^2)^{n-\frac{1}{2}}\cos(xt)dt Prove that ##J_n(x)## satisfies Bessel's...

Homework Statement differential equation (dr/dy)+r=8 ; r(1)=0.3 The Attempt at a Solution (dr/dy)=(8-r) ∫[dr/(8-r)]=∫dy ln|8-r|+c1=y+c2 ; k=c2-c1 ln|8-r|=y+k ; r(1)=0.3 then take of e^ both sides which gives 8-r=e^(y+k) 8-e^(y+k)=r and we know r(1)=0.3 which means...

dm/ds=m ; m(1)=7 when i find the diff eq ∫dm/m=∫ds ln|m|+c1=s+c2 ; k=c2-c1 ln|m|=s+k e ^ both sides m(s)=e^(s+k) ; m(1)=7 m(1)=e^(1)*e^(k)=7 i am stuck here. not sure how to proceed please help.

Homework Statement The power supply in the circuit shown has V(t) = (120V)cos(ωt), where ω = 310 rad/s. Determine the current flowing through the resistor at time t = 9.7 s, given R = 600 Ω, C = 18 mF, and I(0) = 0 A. As a reminder, Kirkhoff’s voltage law for this circuit (Eq. 8-1.3 in the book)...

Homework Statement A spherical mothball of original radius 1.2 cm slowly evaporates such that 180 days later, its radius is only 1 cm. Physically, the rate of evaporation dr/dt is proportional to the surface area of the sphere. Determine a) the time required for the radius of a new mothball to...

Homework Statement dY/dt = y(c - yb) C and B are constants. Im supposed to find and explicit solution for y, but I am having trouble. Homework Equations The Attempt at a Solution dY/y(c - yb) = dt ∫(1/c)dy/y + ∫(b/c)dY/c - yb = ∫dt (i used partial fraction decompositions)...

Hello, I am trying to solve an equation and then execute it in matlab. It is dx/dt=I(S*A*x). so I am trying to see the evolution of x with time. The variables are all in an excel spreadsheet in different columns and the name of the columns are the name of the variables. 'I' is in an...

Hi, I need help in 4 questions. I need their answers if possible.

In a video I was watching regarding how to solve these, the lecturer said that the form of a Bernoulli Differential Equation is y'+P(x)y=q(x)y^n where n>1 This means that if n = 1, it wouldn't be a Bernoulli differential equation and would be a first order linear differential equation, but if...

I understand the derivation for the simple harmonic motion equation: F = -kx ( in a 1-D case) acceleration = x''(t) = (-k/m)x so x''(t) + (k/m)x = 0 But why is the solution to this equation x = A cos (wt + ∅ ) How does one come up with this solution? I tried understanding this by reading...

Whatsup guys, im new in this forum so be easy on me... I've been banging my head against a wall lately... i have come up across a differential equation i haven't been able to resolve... does any of you know any way of resolving this equation?? a(x) needs to be differentiable for any x belonging...

Homework Statement A spring with a spring constant of 20 pounds per foot is loaded with a 10-pound weight and allowed to reach equilibrium. It is then displaced 1 foot downward and released. If the weight experiences a retarding force in pounds equal to four times the velocity at every point...

cosx(dy/dx) + ysinx = sinx cosx (dy/dx) + y/cosx = 1 e^integral (1/cosx) ? I feel like this has to do with ln again but not sure

4y'=e^(x/4) + y First I need to divide through by 4 correct? To obtain y'=(e^(x/4))/4 + (y/4) But then when I try to find integrating factor I just come up with e^(x/4) which I think is incorrect

I have the following differential equation which I obtained from Euler-Lagrange variational principle \frac{\partial}{\partial x}\left(\frac{1}{\sqrt{y}}\frac{dy}{dx}\right)=0 I also have two boundary conditions: y\left(0\right)=y_{1} and y\left(D\right)=y_{2} where D, y_{1} and y_{2} are...

I can't seem to work out this question because it's so weird The set F of all function from R to R is a vector space given the diffential equation f"(x)+3f'(x)+x^2 f(x) = sin(x) is a subspace of F? Justify your answer I know that we have to proof that it's non-empty 0. The zero vector has to...

Is there any material or book that explains how one could go from data to differential equation comprehensively? More like functional data analysis+differential equations

Homework Statement \dot{x} = -pxy + qx, \dot{y} = rxy - sy where p,q,r and s are positive constants (p does not equal r) Question is : Determine all the equilibrium points for the system of differential equations given above, expressing your answers in terms of p,q,r and s The...

Homework Statement Hi there guys I am new to this forum and i have a problem with a bit of cw. It's regarding an RLC circuit. I've come up with a picture (attached) that denotes the equation. Homework Equations I know the equation is L C \frac{d^2 i}{d t^2} + \frac{L}{R} \frac{di}{dt}...

toda is a chain of particles of displacement q(n,t) acoplated by a spring the differential equation are \frac{d^2q(n,t)}{dt^2}=e^{-(q(n,t)-q(n-1,t))}-e^{-(q(n+1,t)-q(n,t))} the solution for one soliton is: q= Cte+ log (\frac{1+cte2 e^{-2cte3 n + 2 sinh t}}{1+cte2 e^{-2cte3 (n+1) + 2...

Hello I need help with the following differential equation: (1-\frac{gh}{c^2}) A(u) - \frac{h^2}{3} A''(u) - \frac{3}{2h} A(u)^2 =0 with g,h,c=constant the answer has a \sech^2 with A(0)=A_0 and A'(0)=0 thanksution[/b]

Homework Statement Can we use y=vx for non-homogeneous differential equation? Example: yy'=x^3+(y^2/x)→not homogeneous Homework Equations y=vx dy/dx=v+x(dv/dx) The Attempt at a Solution By substituting the equation above: vx(v+x dv/dx)=x^3+(v^2 x^2)/x v^2*x+vx^2...

I've separated the variables of this differential equation and end up with dx/((a-x)^(1/2)*(b-c(x-d)^3/2)). I've tried finding the integral of this with non-trig substitution methods but cannot solve it. Any help would be appreciated.

the function obeys the differential equation d^2f/dx^2-(3-2i)f=0 , and satisfy the condition f(0)=1 and f(x)----->o ,for x-----> infinity , for f=0 calculate the value of f(∏)? Can Anybody give me any hints how to go about this problem? What I know is the following; D^2f/Dy^2=(3-2i)f...

Prove that this equation satifies the Euler-bernoulli beam equation which is given by Cany anyone help me with this. Can wolfram alpha do it? It has so many values and I'm not comfartble with doing 4th derivitives

Homework Statement This is a research problem that I imagine is very similar to a homework problem. I am a PhD student in biology, and I lack the mathematical background needed to make sense of the topic. I would like to find the solution to the fractional differential equation that...

Homework Statement dy/dx = 3 - 6x + y - 2xy Homework Equations dy/dx + p(x)y = c p(y) dy = q(x) dx The Attempt at a Solution Just realized where my mistake was, sorry!

Homework Statement Please see attachment Homework Equations Please see attachment The Attempt at a Solution Please see attachment. I am supposed to compare coefficients but it doesn't seem possible. what do I do next? (also, if i have posted this in the wrong forum...I...

I just ran into an interesting problem... which I had wrong :eek: What are the solutions to the following differential equation? $$\frac{dy}{dx} = \sqrt y \qquad \text{with }y(0)=0$$

Homework Statement Homework Statement Solve \frac{dz}{dt} + 3 t e^{t+z} = 0 Homework Equations None that I can think of... The Attempt at a Solution "Rearranging" the given question, we get: \int \frac{dz}{e^z} = -3\int t e^t dt -e^{-z} = -3 \left( t e^t - e^t \right)...

I have the following differential equation \frac{\partial}{\partial t}\left(\frac{a}{X}\right)+\frac{X}{b}\frac{ \partial Y}{\partial t}+\frac{c}{X}=0 where a, b and c are constants and X is a function of t. I want to solve it for Y analytically (if possible) or numerically.

I have the following differential equation \begin{equation} \frac{\partial b}{\partial x}=\frac{b-c}{c^{2}}\end{equation} where b and c are both functions of x. However, although I have a closed form relation between c and x, I do not have such a closed form relation between b and x...

Solve: dx/dt +2y+ex=t2 dy/dt-x+xex=0 Please help for this simultaneous differential equations

Are the equations listed below differential equations? If so, to understand them what level of calculus do I need? I only did alegbra 2 in high school. Δ Wi = η * (D-Y).Ii I(n,EF)=OF(n,EF)*I(n-1,EF) I(1,EF)=OF(1,EF)

Hi

Homework Statement y''+2y'+y=xe-x Homework Equations Yc=c1e-x+c2xe-x relevant info on textbook: "If any term of yp is a solution of the complementary equation, multiply yp by x (or by x2 if necessary)." >> i don't understand the part where it says "a solution of the complementary equation"...

Here is the question: Here is a link to the question: Third order linear differential equation? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement solve: y""+6y'+9y=e-3x/x3 Homework Equations y=yc+yp The Attempt at a Solution I found yc=C1e-3x+C2xe-3x and am having difficulties finding yp. I am wondering which method would be the best to determine yp: - annihilators - undetermined coefficients -...

Homework Statement \frac{d^2 y}{dx^2}\cdot\frac{dy}{dx}=x(x+1), \hspace{10pt} y(0)=1, \hspace{5pt} y'(0)=2 Homework Equations None I can think of... The Attempt at a Solution The only thing I even thought to try was turn it into the form: \frac{d^2 y}{dx^2}{dy}=x(x+1){dx}...

Homework Statement x2y"-(x2+2x)y'+(x+2)y=0 known solutions: y1(2)=2 y1'(2)=1 y2(2)=2e2 y2'(2)=3e2 Determine the wronskian Homework Equations yc=C1er1x+C2er2x I also know how to find the wronskian via a determinant The Attempt at a Solution I have tried to divide out...

Homework Statement A 44 gallon barrel of oil develops a leak at the bottom. Let A(t) be the amount of oil in the barrel at a given time t. Suppose that the amount of oil is decreasing at a rate proportional to the product of the time elapsed and the amount of oil present in the barrel. a...

Homework Statement Given y_1(x)=x is a solution to (2x-1)y''-4xy'+4y=0, find y(2) given (y(1),y'(1))=(0, 0). Utilize method of reduction of order. I need help with this as I end up getting some ugly (in my mind, anyways) integrals. Thanks in advance!The Attempt at a Solution Let y=y_1v=xv...