Homework Statement
Solve:
y'' - λy = 0
where y(0)=y(1)=0, y=y(t)
Homework Equations
The Attempt at a Solution
Hi everyone,
This is part of a PDE question, I just need to solve this particular ODE. I know how to do it in the case for y'' + λy = 0, where you get the...
Homework Statement
I've got
y'' - ω2y = sin(ωx) + sinh(ωx) where y(a) = A, y(b) = B
Homework Equations
The Attempt at a Solution
Yc = C1 Sinh(ωx) + C2 Cosh(ωx)
and I got my Yp to be -1/2*sin(ωx) + 1/2*sinh(ωx)
I'm not sure about getting the Y general. Any pointers...
See the circuit diagram attached.
The voltage source is a sinusoidal AC source with amplitude = 240, Frequency = 50, Phase = 90.
Essentially I have a lab report and I was wondering what sort of equations are required to find the impedance of the circuit. We're not really told if we're...
Hey,
We haven't properly covered this in class yet, but I am trying to study ahead using online course notes, I manage to finish a few questions but I have gotten stuck here,
The question starts by asking for the solution to the ODE:
y' = 1 - 2xy,
When I solve this using the...
Hello Guys!
I have an ODE problem that I'm solving it by MATLAB ODE solvers!
in fact I have a system of non-linear differential equations in one of these equations I have a parameter that it's value is dependent to derivative! the general form of equation is like this (big letter parameters...
If I have y''+y'+2y=sin(x)+cos(x)
can I just say y=Ae^{ix}
and then find y' and y'' and then plug them in and solve for A.
so I get that A= \frac{1}{1+i}
then i multiply and divided by the complex conjugate.
then I back substitute in Eulers formula.
now since I have my...
Well, surely there is one unique solution to linear 1st order ODE and two linearly independent ones for 2nd order linear ODE, but can someone share the proof of this?
hello
this question from my coarse notes has been giving me some trouble so i thought i would ask for some help on here,
http://img88.imageshack.us/img88/9764/asfar.jpg
i understand that since the bases are bases of the same solutions then they are just a multiple of each other, but...
hey guys
i've been trying to work out this ode reduction question,
http://img204.imageshack.us/img204/8198/asdawt.jpg
after i use the hint and end up with a seperable equation then integrate to get
\begin{align}
& p=\pm \frac{1}{\sqrt{{{y}^{2}}-2c}} \\
&...
Hey,
Every where I look I can only find books and pdf talking about the uniqueness and linear independence of the solutions but I haven't been able to find a procedure of finding the solutions to one of these ode's if you haven't been already given a particular solution.
I've been trying...
A "simple" nonlinear ode
Hi
Does anyone see a way to solve/approximate this ODE?
dy'=exp(-f(t)y) with y(0)=yo
f(t) can be as simple as c*t^3/2 but it may be more complex. This came out as the solution of a very complex problem. This is the final threshold.
Thanks,
Donifan
Homework Statement
Need to solve
xy''+y'+xy=0 using Runge Kutta on x[1,3]
Couldn't find algorythm to solve second order ODE using this method
I know how to do 1st order
Homework Equations
The Attempt at a Solution
I know I have to make this equation into 2 first order ODE...
Hey,
I've been trying to solve this ODE using the power series method,
y'' + x^2y = 0,
I end up with (the first sum can start from 0 or 2, i just left it as starting from n=0)
\[\begin{align}
& \sum\limits_{n=0\,}^{\infty }{n(n-1){{a}_{n}}{{x}^{n-2}}+}\sum\limits_{n=0}^{\infty...
Hi,
I'm trying to find a differential equation (first OR 2nd order) whose output could be a Fourier Series of a fundamental frequency input... So It will be a "forced" ODE.
That is, I want
cos({\omega}t) = L[x(t)] where
L is some operator on x(t) such that the solutions in x(t) are...
Homework Statement
Find the specified particular solution:
(x^2+2y')y'' + 2xy' = 0, y(0)=1, y'(0)=0
Homework Equations
The Attempt at a Solution
The equation seems amenable to the substitution p=y', so it can be transformed into (x^2 + 2p)p' + 2xp=0, or (x^2 + 2p)dp + 2xpdp=0. Since...
Problem:
The following two-dimensional system of ODEs possesses a limit-cycle solution for certain values of the parameter$a$. What is the nature of the Hopf bifurcation that occurs at the critical value of $a$ and state what the critical value is.
$\dot{x}=-y+x(a+x^2+(3/2)y^2)$...
Homework Statement
The following two-dimensional system of ODEs possesses a limit-cycle solution for certain values of the parameter a. What is the nature of the Hopf bifurcation that occurs at the critical value of a and state what the critical value is.
Homework Equations...
I have the following ODE system
\begin{cases}
x' = v \\
v' = v - \frac{v^3}{3} - x \\
x(0) = x_0 \\
v(0) = 0
\end{cases}
I am asked to find x_0>0 such that the solution (x(t),v(t)) is periodic. Also, I need to find the period T of such solution.
I don't know how to solve the...
I have:
$\dot{x}=4x+y-x(x^2+y^2)$
$\dot{y}=4y-x-y(x^2+y^2)$
And I need to find $\dot{r}$ and $\dot{\theta}$
I got as far as:
$\dot{x}=r(\text{sin}(\theta)-\text{cos}(\theta)(r^2-4))$
$\dot{y}=r(-\text{sin}(\theta)(r^2-4)-\text{cos}(\theta))$
How do I go from here to $\dot{r}$ and...
Homework Statement
I have:
\dot{x}=4x+y-x(x^2+y^2)
\dot{y}=4y-x-y(x^2+y^2)
And I need to find \dot{r} and \dot{\theta}
2. The attempt at a solution
I got as far as:
\dot{x}=r(\text{sin}(\theta)-\text{cos}(\theta)(r^2-4))
\dot{y}=r(-\text{sin}(\theta)(r^2-4)-\text{cos}(\theta))
How do I...
Homework Statement
For the following differential equation:
1) Provide the general solution
2) Discuss for which values of x the solution is defined.
3) Find the solution of the initial value problem y(0) = 3Homework Equations
dy/dx = (y+3)(y-5)The Attempt at a Solution
1) so I separate...
Hey,
I have been trying to work out how to solve this example question I found in a recommended text,
http://img715.imageshack.us/img715/5052/asdavm.jpg
Everywhere I've been reading starts with since y=eta(x) is a particular solution then y=eta(x) + u is a general solution, but the...
Homework Statement
We are given (1-z)*f'(z)-3*f(z) = 0, f(0) = 2 valid on the open disk centered at 0 with radius 1 and told to prove there is a unique solution to the differential equation. The hint he gave was to find a factor that makes the left side the derivative of a product, but that...
Homework Statement
I wanted to solve a ode which has Brownian motion as a variable coefficient
Homework Equations
2x2y'' + y' -ρy = 0
where x is the Brownian motion with respect to time
ρ is a constant
The Attempt at a Solution
I have tried power series with no solution. Is there a...
Homework Statement
given: (y-xy)y' = y^(2) + 1 y(0)=0
Homework Equations
So I subbed y^(2) = u
The Attempt at a Solution
w/ u=y^(2) i got...
(y-xy)y' = y^(2) + 1
(1-x)yy' = y^(2)
(1-x)(u'/2) = u + 1
and it is here that I am stuck! I [think] I have to put...
Homework Statement
Given the equation mx''+cx=cAsin(Ωt) with the initial conditions x(0)=0 and x'(0)=0.
Solve the initial value problem for the case when Ω < ω and show that |x(t)| < H provided
A < H(1-(Ω/ω)).
Homework Equations
The Attempt at a Solution
For my solution to...
[Ok so I have transformed a
1st order homogenous ODE into a seperable ODE. However I am having trouble seperating to get y on it's own.
Here's the problem:
du/dx=(2u^2)/x where u = y/x
du/(2u^2)=dx/x <<can't get tex to work
-1/(4u^2)=ln(x)+C=ln(Ax) <<can't get tex to work...
I am trying to find a Green's function for a third order ODE.
(\lambda - d3/dx3 - \mu d/dx)u = f(x) with boundary conditions u(0) = uxx(0) = ux(L) = 0 (L is finite).
This has solution u(x) = c1em1x + c2em2x + c3em3x
where m1, m2 and m3 are the roots of the characteristic equation from...
I'm not sure where I'm going wrong on this one so I hoped that I could find some help
we begin with
(x^2 + y^2 + 5) dx - (y+xy) dy
taking both partial derivitives I found that
2y (dy) =/ -y(dx)
Next I went to find my factor of integration using e^(My - Nx / N) dx)This got me ((1+x)^-3)...
Homework Statement
Question
According to Newton’s Law of Cooling, the rate at which a substance cools in air is proportional to the difference between the temperature of the substance and that of air. The differential equation is given byAccording to Newton’s Law of Cooling, the rate at which...
Help solving a second order ODE with repeated roots, urgent!
I have a differential equaition
d2y/dx2 - 6dy/dx + 9y = 0
I have found the general solution to be
y = (Ax + B)e3x
Now I need to find the solutions to A and B so that...
when y = 4, x = 0
when y = 49.e15, x = 5
I...
Ok I'm new to ODE's so yeh, just to double check here's what I've done:
Question: Find the general solution to the following differential equation:
Equation: y'(x) = sec2 (3x + 1)
My answer: Don't I just integrate? So dy/dx = sec2 (3x + 1)
then, y = sec2 (3x + 1) dx
so y = (tan(3x+1))/3
I have been reading Ordinary Differential Equations (Pollard) from Dover.
The chapter I am in, is called Problems Leading to Differential Equations of The First Order - Geometric Problems.
Problem :
Find the family of curves with the property that the area of the region bounded by the...
Homework Statement
I nearly have this problem solved
x2d2y/dx2 + 3x*dy/dx + 5y = 8x
y(1) = 2, y(exp(pi/4)) = 2sinh(pi/4)
I've found the general solution, but I'm not sure how to get the answer with the boundary values
Homework Equations
The Attempt at a Solution
My...
I'm having issues solving a 1st order ODE.
Here what happens:
NDSolve[{y'[x]/y[x] == k *Pi* r^2* Sqrt[1 + y'[x]^2], y[0] == 136/10}, y[x], {x, 0, 30}]
NDSolve::ndnum: Encountered non-numerical value for a derivative at x == 0.
Changing the x range is no help... I get the same message for...
Homework Statement
I just need to know how to start this. I've never seen a piece wise ODE before and I don't really know where to start to be honest. I know it's non-linear and it's of order one.
dy/dx = (1/3)y - 3, y > 0 and dy/dx = -(1/3)y - 3 ≤ 0. y(0) = 1 with y(x) \in C0...
Homework Statement
Let Z={x: {0,1,..,5} → ℝ^n} (column vector with real entries) and define T:Z→ℝ^n by Tz = z(0) - z(5). Let X = Ker(T) and let Y={y: {0,1,..,4}→ℝ^n}. Define L:X→Y by
(Lx)(t) = x(t+1) - Ax(t) where A is an invertible matrix.
Establish criteria for f in Range(L)...
I have to solve this ODE with numerical methods:
(y^2 - 1)\frac{dy}{dx}=3y
I have no initial conditions to solve it like you would normally do. I am hoping to use a numerical method (Euler... Runge Kutta) to approximate the solution. This is if I solve it using numerical methods right? So, I...
Hello all.
I am studying a system and want to investigate how the frequency of y(3) varies under different conditions. However, my the fft I perform on it tells me the frequency is zero, which must be incorrect. I have tried a stack of things but can't see what the problem is. I'm relatively...
How to solve a equation of this kind
T' = a*(T^4 - r^4) + b*(T^4 - s^4) + P*(1 - η(T))
The above equation is driving me nuts... the 'η' is a function of T(Temperature) the efficiency and initial value of T is known.
Say at t = 0 T is 298
Need help! Please!
I need to find the...
Hey all,
there is something that has always bugged me in linear second order ODEs. We say that the general solution is:
y=C_1e^{r_1x}+C_2e^{r_2x}
where r_1 and r_2 are the solutions of the characteristic polynomial.
The cases where r1, r2 are real are pretty straightforward. If they are...
Homework Statement
Find the equilibrium points for the following equation. Determine if the equilibrium points are stable and if stable,approximate the angular frequency.
(i) d2y/dx2 = cosh(x).
Homework Equations
The Attempt at a Solution
For equilibrium points, do we...
Hi all,
I am doing some Laplace Transforms as part of my HND, i have got an answer for this question
q' +2q = 5sint q(0)=0, t(0)=0
But i need to prove it by means of using an integrating factor method.
My original answer is:-
e^-2t +2sint-cost does this look right?
I also have...
Hi.
In the course of trying to solve the field equations of a physical system, within some assumptions about its symetry, i managed to get a non-linear ODE involving only a single function of one variable, but still rather tough to handle :
In the equation, x=x(r) is the unknown function to...
Homework Statement
The slippage of flexible belts over shafts or pulleys of circular cross sections is an important consideration in many mechanical devices. When the frictional contact between the belt and the shaft is about to be broken (that is when the slippage is imminent), a belt drive...
I'm not sure exactly how to solve this ODE. (dx^2)/(dt^2) + (w^2)x = Fsinwt, where x(0) = 0 and X'(0) = 0.
What I've got so far is:
x'' + w^2x = Fsinwt --> x(homogenous) = Acoswt + Bsinwt
I know I have to find a particular solution but I keep getting zero as a result which I know won't...
Hi there,
This ode has me really stumped. Since it is non linear, I don't know which method to use for this:
xy' + 2y = \frac{sec^2(y)}{x}
Thank you :)