Ode Definition and 1000 Threads

Hi. For first order system ODE, complex root. y'=Ay, where A is a 2by2 matrix. I am assuming the roots are complex. After finding the eigenvalue (complex conjugate) and their eigen-vectors (which come in a form of complex conjugate again), we plug into the solution y=ζexp(λt), where λ is...

Homework Statement Find the general solution to ##A(x)y''+A'(x)y'+\frac{y}{A(x)}=0## where A(x) is a known function and y(x) is the unknown one. Hint:Eliminate the term that contains the first derivative. Homework Equations Not sure. The Attempt at a Solution So I don't really...

Homework Statement We have the equation: y'(x)^2+2 (x+1) \left(y'(x)+x\right)+2 y(x)+2 x=0 2. The attempt at a solution None. I don't even know how to proceed with this problem, except for, of course, expansion. I tried the factorization method, but no luck here. I have a feeling I...

Homework Statement I must solve ##y''+2y'+2y=e^{-t}\sin t##. I know variation of parameters might not be the fastest/better way to solve this problem but I wanted to practice it as I never, ever, could solve a DE with it. (Still can't with this one). Though the method is supposed to work...

Homework Statement Hello guys! I've never dealt with an ODE having 2 singularities at once, I tried to solve it but ran out of ideas. I must solve ##(x-2)y''+3y'+4\frac{y}{x^2}=0##. Homework Equations Not sure. The Attempt at a Solution I rewrote the ODE into the form...

Homework Statement Hello guys. I'm totally stuck at finding the solution to ##y'''-12y'+16y=32x-8##. Homework Equations Variation of parameters once I'm done with the general solution to the homogeneous ODE. The Attempt at a Solution First I want to solve the homogeneous ODE...

Hello there, I am solving numerically the ODE $$ \dot{y} = min \, (y, A) + B\, sin(t)$$ , A,B being constant. I obtain a very "wiggled" solution which is very fine to me actually, as it echoes the problem I am studying. However, as the numerical solution scheme is quite "rudimentary" I...

This is surely the simplest problem imaginable in DE, but it's been a few years and I'm having trouble recalling. The goal of my task doesn't necessitate relearning DE, so I thought I would take a shot at asking directly. Simply, I wish to express the time-dependent rate equation...

Homework Statement x d2y(x)/dx2 + dy(x)/dx + 1/4 y(x) Show that the solution can be obtained in terms of Bessel functions J0. Homework Equations Hint: set u = xa where a is not necessarily an integer. Judiciously select a to get y(u). The Attempt at a Solution I tried just...

Homework Statement Find the general solution of the ODE $$ y'' + 16y = 64x \cos x.$$ If ## y(0)=1, y'(0) = 0##, what is the particular solution? The Attempt at a Solution I am confident I can tackle this question, I really just want to check that my particular integral form is correct. I...

Homework Statement I must solve the following diff. eq. ##tx''-(4t+1)x'+(4t+2)x=0## with the initial condition ##x(0)=0## and the relations ##\mathcal {L }[tx]=-\frac{d \mathcal{L}[x]}{ds}##, ##\mathcal {L} [tx']=-\frac{d [s \mathcal {L}[x]]}{ds}## and ##\mathcal{L}[x']=s \mathcal...

I have been thinking about numerical methods for ODEs, and the whole notion of stability confuses me. Take Euler's method for solving an ODE: U_n+1 = U_n + h.A.U_n where U_n = U_n( t ), A is the Jacobian and h is step size. Rearrange: U_n+1 = ( 1 + hA ).U_n This method is...

Homework Statement A full problem description can be found in the attachment (observe the misprint in eq 1). Here follows an outline: We are to study the flow of a fluid through a cylindrical pipe. Two components of Navier Stokes in cylindrical coordinates, with some simplifications...

This is not homework, but rather me just trying to work a numerical analysis problem. I have a second order equation on the form m*y'' = a*y + n*x (no first derivative) How does one convert this? It's been years since I did this. Last I remember, one would start with substituting the...

Solve the differential equation: y(5)+12y(4)+104y(3)+408y''+564y'=0 where the (n) is the nth derivative. So it's a 5th order DE. Now I'm trying to find the roots: One of the roots is r = 0, which I obtain by factoring the equation into this form: r(r4+12r3+104r2+408r+1156) = 0...

Recently I was sent an ODE with the instructions to solve using the annihilator method which I have not used in over 15 years. This is my working, and I was hoping for feedback to see if I have correctly and efficiently applied the method. Here is my working: We are given the ODE: (1)...

Folks, I am trying to understand the balance of units for this eqn ## \displaystyle \frac{d^2}{dx^2}(E(x)I(x) \frac{d^2 w(x)}{dx^2})+c_f(x)w(x)=q(x)## where ##E## is the modulus of Elasticity, ##I## is the second moment of area, ##c_f## is the elastic foundation modulus, ##w## is...

A stiff ODE is defined as one for which the magnitude of the maximum eigenvalue of its Jacobian is much greater than that of the mininmum. It is the real part of the eigenvalue which controls the error in an approximation when a numerical scheme is used to solve the ODE. If it is negative...

Not sure if this topic belongs here, but here goes. Homework Statement From the AP physics C 1995 test there is a problem that gives the potential energy curve U(x). With F=-\frac{dU}{dx} in one variable, F(x)=-\frac{a}{b}+\frac{ba}{x^{2}} Where a and b are constants. Now I need to get...

Homework Statement Show that y(t) = (1/w) ∫[0,t] f(s)*sin(w(t-s)) ds is a particular solution to y'' +w2 y = f(t)where w is a constant. The Attempt at a Solution After wasting several pages of paper I have made virtually no progress. Obviously, substitution suggests you plug in y(t)...

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.

I'm sorry this is going to sound kind of confusing and vague at first but stick with me! I remember a physicsforum thread from long back in which a student posted a test they'd been given back where the instructor marked them off and they argued they were right. The test question was to solve...

Homework Statement Find the solution of the equation: α(dy/dt) + y = f(t) for the following conditions: (a) when f(t) = H(t) where H(t) is the Heaviside step function (b) when f(t) = δ(t) where δ(t) is the delta function (c) when f(t) = β^(-1)e^(t/β)H(t) with β<α Homework...

Find the solution of the equation: α(dy/dt) + y = f(t) for the following conditions: (a) when f(t) = H(t) where H(t) is the Heaviside step function (b) when f(t) = δ(t) where δ(t) is the delta function (c) when f(t) = β^(-1)e^(t/β)H(t) with β<α My try for all 3 are as follow: 1...

Four days ago on mathhelpforum.com the user ssh [I don’t know if he the same as in MHB…] has proposed the following second order complete linear ODE… $\displaystyle y^{\ ''} – \frac{2+x}{x}\ y^{\ ’}\ + \frac{2+x}{x^{2}}\ y = x\ e^{x}$ (1) … and till now no satisfactory solution has been...

I was given the following equation to solve: x^2*y'' + x*y' + k^2*x^2*y = 0 B.C. y'(0)=0, y(1)=0 where k is just some constant. I am having a hard time removing the singularity created by the boundary condition at y' and not aware of a method how. Any advice would be greatly appreciated.

Homework Statement I'm pretty sure this is a typo? http://gyazo.com/802746486cc68852e5384d5a12aed596 Homework Equations See the image ^. The Attempt at a Solution I believe the theorem they're talking about, is that you can write the general solution of a second order ODE : L[y] = y'' +...

Hi all, I'm struggling with this question - I don't really know where to start. So far I have tried putting arbitrary values for 'a' into a quadratic auxiliary equation but using wolfram to calculate the roots gives me complex conjugates that I can't remember a thing about. Question as...

Hi all, I'm struggling with this question - I don't really know where to start. So far I have tried putting arbitrary values for 'a' into a quadratic auxiliary equation but using wolfram to calculate the roots gives me complex conjugates that I can't remember a thing about. Question as...

Suppose I have a really simple first order linear ODE like:$$\dot{\omega} = -k\omega$$ where k is some constant, ω(t) is a function of time that I want to solve for, and the overdot denotes the derivative w.r.t. time. This is really easy to solve, and we all know that with the initial condition...

Homework Statement I have a set of differential equations, which need to be solved by matlabs solvers. all of the states have to stay between 0 and 1, but they don't. I'm 100% sure my equations are right, but MATLAB is taking too big steps, causing the state to go negative or above 1. most...

Ok, here goes: Homework Statement So I've come across this 2nd ODE which I am to "solve ... for a general solution": d^2y / dx^2 - dy/dx + y = cos(x) - sin(x) :-p and then evaluate the "particular solution" using the boundary conditions y=L...

Given $x''-x+x^3+\gamma x' = 0$. Is the below correct? Can I do this? The answer is yes. Let $x_1 = x$ and $x_2 = x'$. Then $x_1' = x_2$. \begin{alignat}{3} x_1' & = & x_2\\ x_2' & = & x_1 - x_1^3 + \gamma x_2 \end{alignat} Then I have the above linear system from the given ODE.

Hello, I am confused as to how to transform nonlinear ODEs to linear ones by change of variables. Usually its pretty straight forward and I can do it, but this particular problem has me stumped and I don't know where to begin. Homework Equations Thank you guys!

I'm trying to figure out how to find the general solution for a simple pendulum with friction. y'' + ky' + (g/L)y = 0 I know how to find the solution for a simple pendulum without friction: y'' = -(g/L)y ... which leads to ... y = Acos((g/L)x) So far I have: y'' + ky' + (g/L)y =...

Homework Statement well the problem is to solve de following differential equation. ##y'^3+(x+2)e^y=0##Homework Equations ##y'=dy/dx=p## The Attempt at a Solution I got this problem in my test today, an i did it just like it is in the image below, but my teacher wasn't sure that it was a...

Homework Statement Consider the family F of circles in the xy-plane (x-c)2+y2=c2 that are tangent to the y-axis at the origin. What is a differential equation that is satisfied by the family of curves orthogonal to F? Homework Equations ∇f(x,y)=<fx,fy> The Attempt at a SolutionMy general...

Homework Statement Find the values of α for which all the solutions of y''-(2α-1)y'+α(α-1)y=0 (a) tend to zero and (b) are ilimited, when t->∞. Homework Equations y''-(2α-1)y'+α(α-1)y=0 => (t)=Ae^{αt}+Be^{(α-1)t} The Attempt at a Solution I found that the general solution to the...

Homework Statement So yeah, my first time playing with ODEs, how exciting. So my prof gave us a few suggested exercises and I want to know whether I'm actually doing these properly or not. The question and all relevant things will be included in the picture below ...

1. y''y^4 = 8 I tried almost every method I know, including laplace transforms, variation of parameters, reductin of order, v=y' substitution

Homework Statement In a HW assignment, I'm given the ODE y' = f(x,y,\epsilon) and that y = \phi(x,\epsilon) is a solution to this equation. I'm then asked, is \phi(x,0) a solution to the equation y' = f(x,y,0) This result is used for the second part of the problem, and in...

For the scalar linear ODE with periodic coefficients, $$ x' = a(t)x,\quad\quad a(t + T) = a(t), $$ show that the solution is of the form $$ x(t) = x_0e^{\mu t}p(t), $$ where $\mu$ and $x_0$ are constants, and $p(t)$ is a $T$-periodic function. How can I show the solution is of the form...

Hi, The final step of solving a separable ODE is to find a function, f, defined implicitly by a relation G(y) = H(x). Say G(y) isn't defined at y = a and H(x) isn't defined at x = b, it appears to me that when rearranging such a relation to put y in terms of x, the point at which G(y) isn't...

Homework Statement Hi I am trying to solve the following system of ODE's by Laplace transforming: x' = 1 + 21y - 6x \\ y' = 6x-53y with the initial conditions x(0)=y(0)=0. Laplace transforming gives me (X and Y denote the Laplace transformed variables) sX = 1 + 21y-6x \\ sY = 6x-53y From...

Help solving this ODE [SOLVED] Homework Statement \frac{dy}{dx} = \frac{e^{-x}cosy - e^{2y}cosx}{-e^{-x}siny+2e^{2y}sinx} Homework Equations The Attempt at a Solution First, this is non-linear, not a bernoulli, non-separable, and looks hopeful for an exact. But when I take the...

For example, ODE: y'' + y = 0 solve this problem using MAPLE f(x) = _C1*sin(x)+_C2*cos(x) My question is Eigenvalue for D^2+1=0 is +i, -i so general solution is f(x) = C1*exp(i*x)+C2*exp(-i*x) according to Euler's formula f(x) = C1( cos(x)+i*sin(x) ) + C2*( cos(x)-i*sin(x) ) it is different...

Hi, I am completely stuck on this problem that has been given to us. I must solve a set of 2nd order differential equations using Euler's method. It is for a geosychronous orbit of a satellite, meaning the orbit is circular and the velocity vector is perpendicular to the radius vector...

Homework Statement Working with a fluids problem I have derived a pde in v(y,t). It does not seem to matter but I'll write the PDE I derived, in case: \frac{\partial v}{\partial t}=\upsilon \frac{\partial ^2 v}{\partial y^2} Assuming I know that the similarity solution below will work...

Homework Statement A culture of bacteria have a growth rate (as a percent) given by kb per year, constant k>0 and b is the number of bacteria. A virus removes bacteria at a rate of m bacteria per year. I am trying to model this information using an ODE, but might be making a mistake. Homework...