Ode Definition and 1000 Threads

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...

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...

Homework Statement I have the ODE y' = f(\frac{y}{x}) , and I want to re-write this as a separable equation using the change of variable u = \frac{y}{x} The Attempt at a Solution I use the chain rule to write y' = \frac{dy}{dx} = \frac{dy}{du}\frac{du}{dx} = \frac{dy}{du}(-\frac{y}{x^2})...

Hi all Quick one, if one had an equation y' = x on could simply separate the variables and integrate. Now it the equation y'' = x you would use separation of variables what drives this? Also y'' =0. Is the same as. y''dx =0 dx Why is this legal?Thanks in advance

Homework Statement Solve the piecewise linear ODE, y' - y = f(x), y(0) = 1, where f(x) = 1 when 0<=x<=1 and f(x) = -1 when x > 1. y(2) = ? Homework Equations None The Attempt at a Solution I found the integrating factor to be e^-x and multiplied both sides of the equation by the...

$y''+y=\alpha\cos x + \cos^3x$ What value of $\alpha$ makes this resonance free? $\cos^3 x = \frac{1}{4}\cos 3x+\frac{3}{4}\cos x$ So $y''+y=(\alpha+\frac{3}{4})\cos x + \frac{1}{4}\cos 3x$ What am I supposed to do to find alpha?

Homework Statement I want to find the general solution for y(x) if dy/dx = x + y^2 with initial cond't y(1) = 2 Homework Equations The Attempt at a Solution I can't figure out how to make it linear. (Obviously I don't think it's seperable) Any suggestions/solutions...

$y' = \begin{pmatrix}1 & 2\\ 0 & 1\end{pmatrix}y$ The characteristic equation is $$ \lambda^2 - 2\lambda + 1 = (\lambda - 1)^2 = 0. $$ So the eigenvalues are $\lambda_{1,2} = 1$. Solving $(1 - \lambda)y_1 + 2y_2 = 0\iff y_2 = -\dfrac{1}{2}(1 - \lambda)y_1$, we have $$ y = \begin{pmatrix} 1\\...

$y''+y = e^{it}+e^{3it}$ Solution $y = Ae^{it}-\dfrac{1}{8}e^{3it}-\dfrac{it}{2}e^{it}$ and $y''+4y=1+\sin t+\sin 2t$ Solution $y=A\cos 2t + B\sin 2t + \dfrac{1}{4} + \dfrac{1}{3}\sin t - \dfrac{t}{4}\cos 2t$ Correct?

Is there a general solution to \frac{d}{dt}\left[p(t)\frac{dx(t)}{dt}\right] + q(t)x(t) = 0 for x(t) when p(t) and q(t) are arbitrary functions? Better yet, does this question have a name, or some identifier, that I could look in to? It might appear more familiar written as...

Hi All I am rusty with my my math and got stumped with a straight forward question regarding vibrations and complex roots. I have a 2nd order ODE x'' +4 x' + 16 x = some forcing funciton This turns out complex roots. I go through the run around of solving this and I get a...

I'm trying to find a power law relationship between mass and metabolic rate, given that each of these quantities is defined by a differential equation. Assuming dM/dt=a*M(t) and dR/dt=b*R(t), where M(t) is mass and R(t) is metabolic rate, I know that I can solve each of these equations to...

A car of mass 1200 kg is started from rest and pulled on the level ground by an engine. The resistance of the motion is Kv, where v(m/s) is the velocity of the car at time t(s). The power of the engine is constant and equal to 80000 watts. a) How does P, the power of the engine connect to F...

Hi all, I'm trying to use MATLAB to obtain simulations for some equations that describe a model. I'm new to MATLAB (though I've taken a course in C++ and another in Java), so I read a bit on the mathworks website on solving ODEs, and settled on [FONT="Courier New"]ode45 The equations I'm...

Hi everyone, I have a problem understanding an ODE and using it to find something particular. Consider the following : ODE : dC/dt= S-r*C where S: synthesis rate r : death rate C: population Co: initial population the analystical solution is simply C(t) =S/r -(S/r-Co)*exp(-r*t)...

Homework Statement I'm reading a chapter out of Elem. DE 6th Edition by Rainville and Bedient (Ch 4 pg 61) titled integrating factors found by inspection. To explain it, the authors start with an equation, which is grouped to become: y dx + x dy + x^3y^2 dy = 0 which then becomes...

I am not too familiar with differential equations but am familiar with basic calculus, I came across this equation trying to describe a particular function: dy/dx =((sqrt((y-x)^2+y^2)-abs(y))/(y-x))*abs(y)/y Anyway I tried to separate the variables unsuccessfully and using v(x)=y(x)/x with...

Homework Statement Find the Taylor expansion y(x) satisfying: y'(x) = 1 - xy Homework Equations The Attempt at a Solution So I need expressions for y''(x), y'''(x), ...etc I can find y''(x)=-y-xy' by differentiating implicitly. By setting y'(x)=z, then dz/dx =...

hi all, I've been trying to work this problem out, \frac{dv}{dt}-A(B-v)^{1.6}=G A, B and G are constants and Matlab can't give me a solution either. I'm wondering if there is even a solution?

second ODE, initial conditions are zeros at infinity! I want to know the temperature profile of phase transition layer in the interstellar medium. For stationary solution, the dimensionless differential equation I ended up with is \frac{d^2T}{dx^2} = \frac{f(T)}{T^2} - \frac{1}{T} where f(T)...

Hello, I'm having hard times with the following simple linear ODE coming from a control problem: $$u(t)' \leq \alpha(t) - u(t)\,,\quad u(0) = u_0 > 0$$ with a given smooth α(t) satisfying $$0 \leq \alpha(t) \leq u(t) \quad\mbox{for all } t\geq 0.$$ My intuition is that $$\lim_{t\to\infty}...

Question: For the interval x > 0 and the function set S = { 3ln(x), ln2, ln(x), ln(5x)}, construct a linear ODE of the lowest order. My work: Taking the wronskian for this solution set, I get it as 0. Doesn't that mean that a linear ODE for this set cannot be found? I'm very confused here...

currently i am a math major, still unsure whether pure or applied. i am also looking to double major in physics. which class would be more helpful to me: abstract algebra, or (upper division) ODE class? I have taken the lower division DE class already.

A problem from a heat transfer book with conduction and radiation led me to a differential equation like this: T'(t) = a - b*T(t) - c*T(t)^4 Although my professor said that there wouldn't be an analytical solution for this one and to get the answer by an iterative method I got curious and...

Hi all, I've written a simulation of water flow in two dimensions in F90 but I'm having some trouble with it. Water flows from one cell to another using an equation for rate of change of depth and an algorithm for assigning flow direction. The flow direction bit is fine but the dD/dt...

Hello! On Pauls notes webpage, there is the following problem to be solved by variation of parameters: ty''-(t+1)y'+y=t^2 (1) On the page, the fundamental set of solutions if formed on the basis of the complementary solution. The set is: y_{1}(t)=e^t and y_{2}(t)=t+1 Now, I must be...

I got trouble in dealing with this kind of system. For example, Ay``+By`+Cy=0 where y=transpose(y1 y2) A=(1 0 0 1) B=(0 1 1 0) C=(1 1 1 1) May someone give me a book name?:smile:

2nd Order Homogenous ODE (Two solutions??) Alright. I understand that if we have a differential equation of the form A\cdot\frac{d^{2}y}{dt}+B\cdot\frac{dy}{dt}+C\cdot y = 0 and it has the solution y1(t), and y2 is also a solution. Then any combination of the two yH=C1y1(t)+C2y2(t)...

They give a differential equation: x' = f_a(x) = ax(1-x) . In determining if the equilibrium points are sources or sinks, they say: We may also determine this information analytically. We have f'_a(x) = a - 2ax How can they differentiate with respect to x? x is a function, it doesn't...

Hi, I am a newbie to matlab I have 4 equations ode to a system, dxdt=-c*z*s') dydt=((-1.021*(y^2))/(b+a))-(2.081015257+(6.936717523*x))/(b+a)+((p*r)-(p*j)/(b+a))-(((p^2)-2*p*(s^2)*c*z^2))/2*p')...

I feel very comfortable doing this because I've taken numerical analysis and written a short term paper on numerical approximations for PDEs. I am very strong in linear algebra and have calc I/II. The reason I ask for advice is because I have just graduated from undergrad with a degree in...

I have a pesky problem, I have this function of time, S(t) and I'm trying to find how far to evaluate S (its an expensive process and must be done for finite t=time). Essentially, I want to measure S until dS/dt ≈ 0. But my current criteria is making the computation itself inefficient not to...

How to use Matlab ODE solver "events" to stop an integration I'm using Matlab's ODE solver (specifically ode15s) to solve a system of equations. The sum of the values of the equations eventually arrive at a steady state, but the time at which that occurs is dependent on several things, not...

Homework Statement I have not had luck in finding a solution that describes an object falling. Forces include gravitational force which is constant and a vicous force directly proportional to the cube of the velocity. I am supposed to find v as a function of time.Homework Equations v' +...

Hi, I'm not sure if this is on the right thread but here goes. It's a perturbation type problem. Consider the boundry value problem $$\epsilon y'' + y' + y = 0$$ Show that if $$\epsilon = 0$$ the first order constant coefficient equation has the solution $$y_{outer} (x) = e^{1-x} $$...