Ode Definition and 1000 Threads

Homework Statement Solve: y''+λ^2y = cos(λt), y(0) = 1, y'(π/λ) = 1 where t > 0 Homework EquationsThe Attempt at a Solution I start off by taking the Laplace transform of both sides. I get: L(y) = \frac{s}{(s^2+λ^2)^2}+\frac{sy(0)}{s^2+λ^2}+\frac{y'(0)} {s^2+λ^2} Now take the inverse...

Homework Statement Find the general solution y"+3y'+2y=0 Homework Equations y(t) =c_1e^r_1t + c_2e^r_2t The Attempt at a Solution a=1 b=3 c=2 r^2+3r+2=0 (r+2)(r+1)=0 r_1=-2 r_2=-1 General solution: y(t) =c_1e^(-2t)+c_2e^(-t)I was wondering if the order mattered. The answer in the book is...

Problem: y'=((x-1)/(x^2))*(y^2) , y(1)=1 . Find solutions satisfying the initial condition, and determine the intervals where they exist and where they are unique. Attempt at solution: Let f(x,y)=((x-1)/(x^2))*(y^2), which is continuous near any (x0,y0) provided x0≠0 so a solution with y(x0)=y0...

Homework Statement Find a particular solution to: (3x+2y+3)dx - (x+2y-1)dy = 0, y(-2) = 1 The answer to this problem as presented in the book ODE by Tenenbaum is the following: (2x+2y+1)(3x-2y+9)^4=-1. Homework Equations I will be shifting the origin to try to compute this problem. The...

Solve the ode $$(y-2x^2y)dx +xdy = 0$$ The equation is in exact form $$Q(x,y)dx+ P(x,y)dy =0$$ When I test for exactness it fails. Then I used the technique $$\frac{M_y-N_x}{N}$$ I get $u(x)=-2x$ as my integrating factor. But I end still end up with a non-exact d.e why is that...

Hi PF! Anyone have any ideas for a solution to this $$0 = F F''+\left.2F'\right.^2+ xF' + F$$ where primes denote derivatives with respect to ##x##. So far I have tried this $$0=\left( F F'\right)'+\left({xF}\right)'+\left.F'\right.^2$$ Which obviously failed. I also thought of this...

Hi Could someone please help me to understand what questions a) and b) here are asking for?

Homework Statement Uxx - SU = A ; 0<x<1 Boundary conditions : Ux(0) = 0 U(1) = 0 The Attempt at a Solution I tried to set a new variable W = u + A, I can get rid of the A in the main equation and U(1) becomes = 1. If I set U= C*esqrt(S)x into the equation, its a trivial solution because of...

Use laplace Transform to solve this ode: So I got: sV(s)-V(0)-12V(s)=U(s+5) V(s)(s-12)=U(s+5)+1 V(s)=[U(s+5)+1]/(s-12) Now to go back to time domain with Inverse Laplace Transform...My question is, how to transform U(s+5)/(s-12)? Any help? Thanks guys

consider ODE : Show that the solution to this ODE is: Can someone tell what kind of ODE is it?I thought,it's on the form of Bernoulli ODE with P(x)=0.Is it possible to still solve it by using Bernoulli Methodology?I mean by substituting u=y^1-a with a=2? Thanks

I have been solving system of homogeneous ODE numerically using Crank-nicolson (CN) method but now I have a system of non-homogeneous ODE. It would seem that CN would not work since the rank of the matrix will be less than the dimension of the matrix. Is there any other method that can...

Is there an approach to the following 2nd order nonlinear ODE? xy'' + 2 y' = y^2 - k^2 I am interested in learning how to analyze for asymptotic behavior, proof of existence, etc.

Hi there, I was just trying to perform a change of variable on a differential equation as shown below. The original second order ODE is written in terms of a dependent variable ## \theta ## and independent variable ##q##. I have used the expression ## q = \sqrt{\frac{z\tau'}{LT_R}} ## and...

I am trying to find the steady states in the ODE system. Assuming y0 = 2.5 * 10^5, I want to calculate y1, y2, y3 at the steady state. I do not understand how this would be possible, because only y0 is given and the following: d0 = 0.003, d1 = 0.008, d2 = 0.05, d3 = 1, ry = 0.008, ay = 1.6/100...

Homework Statement Solve the following equation. Homework Equations ( 3x2y4 + 2xy ) dx + ( 2x3y3 - x2 ) dy = 0 The Attempt at a Solution M = ( 3xy4 + 2xy ) N = ( 2x3y3 - x2 ) ∂M/∂y = 12x2y3 + 2x ∂N/∂x = 6x2y3 - 2x Then this equation looks like that the integrating factor is (xM-yN). IF =...

I think I am missing something painfully obvious, but what exactly is the difference in algorithms used to solve PDEs vs ODEs? For example, I've been looking at finite difference methods and the general steps (from what I've seen, although particular approaches may vary) used to numerically...

Could someone tell me an application of the model of free fall to industry or more generally by using Newton's second law and the law of gravitation, construct a model similar to the free fall one, that has an application in industry

Homework Statement $$y''+6y^{2/3}=0$$ Homework Equations Nothing comes to mind The Attempt at a Solution I don't really know where to start. Any tricks or tips are appreciated. This isn't a homework question, but I posted here since I didn't know where else to post. Thanks for your time

I have a trouble with ODE, I try to find asymptotic solution for odes which presented in pics. But I can’t. Please introduce a method which I solve these equations. I can solve these equations analytically but after solution, inverse Laplace transform must apply to find final answer. In...

Hi PF! Suppost I had some differential equation, say $$y'(x) + axy(x) +7a =0$$ where ##y=f(x)## and ##a## is some parameter. How do you reference this differential equation with different ##a## values are plugged in? Would I say $$ F(x,y;a) \equiv y'(x) + axy(x) +7a =0$$ and then when...

Homework Statement This is for differential equations with nonconstant coefficients and I wasn't so great at series and sequences in calculus so when I came across this example problem I wasn't sure how they got to their final form. If someone could explain it to me that would be really...

Homework Statement \frac{d\vec{Y}}{dt} = \begin{bmatrix} 0 & 2\\ -2 &-1 \end{bmatrix}\vec{Y} With an initial condition of \vec{Y_0} = (-1,1)[/B] a) Find the eigenvalues b) Determine if the origin is a spiral sink, source, or center c) Determine the natural period and frequency of the...

Kreyszig Advanced Engineering Mathematics shows the variation of parameter method for a system of first order ODE: \underline{y}' = \underline{A}(x)\underline{y} + \underline{g}(x) The particular solution is: \underline{y}_p = \underline{Y}(x)\underline{u}(x) where \underline{Y}(x) is the...

Good morning everyone. First let me thank you for your help in advance! I have to solve this 2nd order non-linear ODE, and I'm stuck at the beginning. We have to find the equilibrium points, linearize the system, draw the phase portraits and classify the eq points, and solve it numerically. I...

Homework Statement x²y''+xy'+(x²-0,25)y=0 y1= x^-1/2*sin xHomework Equations Abel's equation: W= c.e^-(integrate (p(t))The Attempt at a Solution My Wronskian gave me a first order ODE that I really don't know solve. x^-1/2*sinx y' + (1/2 x^-3/2 sin x- x^-1/2cosx) y2 I don't solved the Abel's...

Hi there dr/dz+z^2=0 is classified as a non-homogeneous in Glyn James text, can someone clarify this? Cheers Petra d.

Homework Statement Solve for xy'' + y' +αy + βxy = 0 α and β are constants The Attempt at a Solution What I initially had in mind was: xy'' + y' +αy + βxy = x²y'' + xy' +αxy + βx²y = 0 y = \sum_{n=0}^\infty a_n x^{n} xy = \sum_{n=0}^\infty a_n x^{n+1} = \sum_{n=1}^\infty a_{n-1} x^{n} = a_0x...

For ordinary differential equation y''(x)+V(x)y(x)+const y(x)=0 for which ##\lim_{x \to \pm \infty}=0## if we have that in some point ##x_0## the following statement is true ##y(x_0)=y'(x_0)=0## is then function ##y(x)=0## everywhere?

Hi I am trying to understand numerical analysis on my freetime and today I studyed how to solve y' = \frac{x^2}{1 + y\sin (y^2)}, with initial value y(0) = 0. I asked myself two simple questions: What is y(1.5) and what is y(2.5)? As for to check the answers, I solved the ODE. In implicit form...

Hey all, I want to try and pass a proficiency exam for my universities version of ode. Here (http://www.math.uiuc.edu/Bourbaki/Syllabi/syl285_edwards-penney.html). What book would you all recommend? (I prefer rigor, but also like ease of read if there is a good middle ground). I will only...

Homework Statement \frac{dy}{dx}=y^2-1 y(0)=3 Homework Equations \frac{dy}{dx}=f(y) \leftrightarrow \frac{dx}{dy}=\frac{1}{f(y)} The Attempt at a Solution \frac{dx}{dy}=\frac{1}{y^2-1} dx=\frac{dy}{y^2-1} \int dx=\int \frac{dy}{y^2-1}+C x=\int \frac{dy}{y^2-1}+C How do I integrate \int...

Hi, I am looking for good books with somewhat of an intuitive explanation on waves physics (acoustic waves), elastic waves, on ODEs, PDEs, and calculus? Also some good ones on DSP Thanks in advance Chirag

Homework Statement I want to find conditions over A,B,C,D to observe a stable limit cycle in the following system: \frac{dx}{dt} = x \; (A-B y) \hspace{1cm} \frac{dy}{dt} = -y \; (C-D x) Homework Equations Setting dx/dt=0 and dy/dt=0 you can find that (C/D , A/B) is a fixpoint. The Attempt...

MX''=Fn(cosΦ−usinΦ) MZ''=Fn(sinΦ+ucosΦ)−Mg MΦ''=Fn(Bxx+uBz) I tried using Runge-Kutta methods to approximate motion equations in MATLAB but it turn out wrong. I also tired finding and researching forums and web for solution but to no avail. Fn,M,θ,u is constant fn/M = 0.866 it seems that i...

I am studying ode now, and my text has that If y'=f(y/x) Then, setting y/x=u ; y=ux is a way to solve it. I understand the idea, turn orignal form to separable form. But I can't get the differentiation, Book says y'=u'x+u by product rule which I already know. Here my question is why u=y/x that...

Homework Statement Hi There! MX''=Fn(sin θ - uCos θ ) MZ''=Fn(cos θ + uSin θ ) - Mg Fn,M,θ,u is constant fn/M = 0.866 M = 6000 θ = 30 u = 0.5774 i split my motion equation into 2 individual 1st ode, X' = Vx Z' = Vz Vx'=[fn*(sin θ - uCos θ )]/M Vz'={[fn(cos θ + uSin θ )]/M} - g...

Let’s consider Uc to be transformed form of h(x,t) by applying Fourier transform Then solution of Eq 1 by integrating factor is as in Eq 2 And by applying on Eq 2 inverse Fourier transform & some simplification gives us final solution as Eq 3 But what if f(t) in Eq 1 is equal to Eq 4 Putting...

Homework Statement A time-dependent two-dimensional fluid flow is given, in a Cartesian coordinates system (x, y), by the velocity field: u = (y, t-x) Show that, at time t = 0, the streamlines of this flow are circles centred on the origin. Find equation of the streamline that passes through...

The question is as follows: Suppose you find an implicit solution y(t) to a first order ODE by finding a function H(y, t) such that H(y(t), t) = 0 for all t in the domain. Suppose your friend tries to solve the same ODE and comes up with a different function F(y, t) such that F(y(t), t) = 0 for...

I'm supposed determine whether following statements are true or false. However, I can't get past the notation. Question: the second order differential equation $\ddot{x}+\dot{x}+x = 9t$ is: (a) equivalent to $\begin{cases} \dot{x} = y, & \\ \dot{y}=-y-x+9t, &\end{cases}$ (b) solved by...

I'm trying to solve $\displaystyle x(y-3x)\frac{dy}{dx} = 2y^2-9xy+8x^2$ Let $y = vx$ then $\displaystyle \frac{dy}{dx}= v+x\frac{dv}{dx}$ and I end up with $\displaystyle \log(cx) = \frac{1}{2}\log(y^2/x^2-6y/x+8)$ Is this correct and what am I supposed to do after this?

I am having a little trouble with a problem I am trying to solve. Given three particular solutions Y1(x)= 1, Y2(x)= x and Y3(x)= x^2 Write down a general solution to the second order non homogeneous differential equation. What I have done so far is to realize if Y1,2 and 3 are solutions...

{ i feel that this is Not a smart question and that it is about the basics of something , but i tried to find the that "something" to know about it myself but i couldn't , as i couldn't name the issue , so i couldn't know what to search about that is why I'm asking here in a forum , so please...

Frobenius method - recurrance relation question If, using the Frobenius method, I get a 3 term recurrence relation of the form $a_{j+2} = a_j .f(k,j) + a_{j-2}. g(k,j)$ ( j even), how do I treat the $a_{j-2}$ term at first? I have found $a_1 = 0$, but how do I find a value for $a_{-2}$ so as...

Im stuck on this question, can someone please help me? u(t) = input power [W]. x(t) = temperature in plate [Celsius] v = 0, temperature of surroundings [Celsius] C = 400, heat capacity for plate [J/ Celsius] g = 2, heat transfer plate / air [W / Celsius] Question is something like this: You're...

Homework Statement Find the general solution f(t) of the differential equation: f''(t) − f'(t) − 12f(t) = 36π . How many free parameters enter the solution, and why? Homework Equations f = fH + fP where fH is the homogeneous solution and fP is the particular solution. The Attempt at a...

Hi - I'm given: $ y'' + y' - 2y = \frac{e^{x}}{x} $ What is a good Ansatz to find the particular solution? I've tried a few that haven't worked...Thanks

Given $ x^2y'' + xy' - n^2y = 0 $ I think this is an Euler ODE, so I try $y=x^p, \therefore y'=p x^{p-1}, \therefore y''= p (p-1) x^{p-2}$ Substituting: $x^p p(p-1) + x^p p - n^2 x^p = 0, \therefore p^2 = n^2, \therefore p= \pm n$ $ \therefore y=C_1 x^n + C_2 x^{-n} $?

Homework Statement Use Laplace transform to solve the following ODE Homework Equations xy'' + y' + 4xy = 0, y(0) = 3, y'(0) = 0 The Attempt at a Solution L(xy'') = -\frac{dL(y'')}{ds} L(4xy) = -\frac{4dL(y)}{ds} L(y'') = s²L(y) - sy(0) - y'(0) = s²L(y) -3s L(y') = sL(y) - sy(0) - y(0) =...

The ODE is $y'' + 4y' - 12y = 0$, I get $y = C_1e^{-6x} + C_2e^{2} $ The initial conditions are y(0) = 1, y(1)=2 - which gives me $C_1 = 1-C_2$ and $C_2 = \frac{2e^{6}-1}{e^{8}-1} $ This just looks more messy than book exercises normally are, and when I laboriously substitute back into the...