Odes Definition and 227 Threads

Are PDEs or ODEs more useful? Especially in biochemistry/molecular biology. Would learning PDEs also allow one to deal with ODEs?

Hey everyone. I'm trying to refresh myself of solving linear ODEs. For simplicity's sake, I began by trying to solve xy'=xy+y This is actually a separable ODE, and the solution is y = c_{1}xe^{x}. I am attempting to derive the same result from a series solution. First, rewrite this as a...

I am looking through my course notes for mathematical physics, in preparation for the exam, and I've run into a concept that I can't figure out. It comes up first when talking about the modified bessel's equation (x^2)y''+(x)y'-(x^2+p^2)y=0 And supposedly this can be transformed into...

Homework Statement I'm trying to solve the following system of ODEs. \alpha = \alpha (r) \alpha ' + \frac{n-1}{2r} \alpha =0 \alpha '' + \frac{n-1}{r} \alpha ' = 0 The attempt at a solution The solution to the first one is \alpha = r^{\frac{-(n-1)}{2} The solution to the...

Homework Statement I am asked to solve a coupled system of 5 ODEs. There is also a function, f, which describes the release of carbon dioxide over time. I am given the release rates at certain values of t and asked to interpolate for other values of t in the interval [1000 3000]. After...

Homework Statement I'm trying to solve the equations: \ddot{\phi} + 2\left(\frac{\cos \theta}{\sin \theta}\right) \dot{\theta}\dot{\phi} =0 and \ddot{\theta} - \sin \theta \cos \theta \dot{\phi^2} =0 for \theta(\lambda), \phi(\lambda) where the dots represent differentiation w.r.t...

I know that a 2nd order homo ordinary differential equation's solution is in the form of \[f(x) = {C_1}{e^{{a}t}} + {C_2}t{e^{{a}t}}\] for repeated real roots of the characteristic equation, and that the solution for a single complex root (and its conjugate) involves a cosine. I'm curious...

Homework Statement Solve this system of linear ODEs: 1) x''(t) = x + y 2) y''(t) = x + y Just fyi, this is part of a much larger problem but I need to solve this system! Homework Equations See above. The Attempt at a Solution Okay so I think the most logical way to solve...

Homework Statement Two identical masses m1 = m2 = m are connected by a massless spring with spring constant k. Mass m1 is attached to a support by another massless spring with spring constant 2k. The masses and springs lie along the horizontal x-axis on a smooth surface. The masses and...

Homework Statement 6x2(x+1)2y''+0.5x(x+2)y'+y=0 ii) Find all values of r for which there is a series solution of form xr\sum(anxn,n=0,inf) a0 \neq0 Find all values of r for which there is a series solution of form inf xr\suman(x-2)n...

How to solve two nonlinear ODEs with boundary conditions? Here is the Q:

Can anyone help me to get the general solution of the linear partial differential equations with variable coefficients of any order?

Homework Statement Solve (x - \sqrt{xy})dy - ydx = 0 Rearranged gives us -y + (x - \sqrt{xy})y' = 0 And it looks like an exact differential equation, but is it really? Homework Equations For any given exact equation of the form M(x,y) + N(x,y)y' = 0 The following must be true...

I have been working on a derivation in which the following simultateous ordinary differential equations have appeared: f^{(4)}(x)-2 a^2 f''(x)+a^4 f(x)+b(g''(x)-a^2 g(x))=0, g^{(4)}(x)-2 a^2 g''(x)+a^4 g(x)-b(f''(x)-a^2 f(x))=0, where a and b are constants. I figured that I could solve...

Ok, so I've been studying the method of variation of parameters in order to solve 2nd order ODEs, and I have a question regarding a supposition that is made in the definition of the method. Say, y'' + p(t)y' + q(t)y = g(t) Then the general solution to the above equation is c_1y_1(t) +...

Homework Statement I need to annihilate ln(x) Homework Equations The Attempt at a Solution my try was saying that this is a eular equation with r1=r2=0 c1=0 and c2=1 so the annihilator should be D^2 but I don't think it works. Any other suggestions ? Thanks.

Homework Statement In a problem I was given a system of three differential equations concerning three functions, x(t), y(t) and z(t): dx(t)=2y(t)dt, dy(t)=[z(t)-x(t)]dt, dz(t)=[c^2x(t)-2y(t)]dt. (where c is a constant) The problem asked me to prove that when t is large, x(t)+z(t)...

Hello All, I am stuck on the following question. Can you please help to find the solutions Using the complementary function and particular integral method, find the solution of the diffential equation which satisfies y(0) = 1 and y'(0) = 0. y'' + 3y' + 2y = 20cos2x and then can you...

Homework Statement I have a problem in solving a system of two ODEs for BVP 1. Pb is function of X & A 2. A is a function of X,Pb,A 3. BCs are X = 1, Pb = 0, A = 0.441 X = 0, Pb = 0 Q is a variable to achieve the other end BC I have tried to use ODE...

I have a somewhat theoretical question regarding Differential Equations: How can we reconcile the fact that if I go from let's say this system of 1st ODE x' = 2y-x y' = -x+y to a 2nd ODE "using x(t) instead of y(t)" we get: x" + x =0 then back to a system of 1st ODE: letting...

Could someone explain why the graph of a solution can never cross a critical point?

1. Using the complementary function and particular integral method find the solutio of the differential equation. d2y/dx^2 + 3 dy/dx +2y = 20cos2x Which satisfies y(0) = 1 y'(0) = 0 Homework Equations The Attempt at a Solution

Homework Statement How can I annihilate the following ? 4e-2t*cos(2t) Homework Equations The Attempt at a Solution I know that if I want to annihilate e-t it would be (D-1) and to annihilate cos(2t) it would be (D2+22) but what happens if they are multiplied ? how do I...

I want to know if there is a general solution to a second order homogeneous differential equation with variable coefficients?

Homework Statement 1)Find the solution of x'=x^{\frac{1}{2}} that passes through the point (t_0, x_0) where x_0>0. 2)Find all the solutions of this equation that pass through the point (t_0,0). Homework Equations Direct integration. The Attempt at a Solution...

Homework Statement Verify that the differential operator defined by L[y] = y(n) + p1(t)y(n−1) +· · ·+ pn(t)y is a linear differential operator. That is, show that L[c1y1+ c2 y2] = c1L[y1] + c2L[y2], where y1 and y2 are n times differentiable functions and c1 and c2 are arbitrary...

Hi guys, I really have no idea how to approach finding the particular integral for, say: f'' + 5f' + f= e^x sinx Could anyone help me? And for future reference how do you go about finding the PI for any combination of polynomials/exponentials/sinusoidals? Thanks in advance for the help!

I have the following coupled ODE: 2x+y^2=d^2x/dt^2 2y+x^2=d^2y/dt^2 How would one solve for x(t), y(t)?

Hi guys, i have 4-coupled ode's that are giving trouble (1) \frac{dy_1}{dt}=y_2y_3-\mu y_1, \hspace{1cm} \\(2) \frac{dy_2}{dt}=y_1y_4-\mu y_2, \hspace{1cm} \\(3) \frac{dy_3}{dt}=1-y_1y_2, \hspace{1cm} \\(4) \frac{dy_4}{dt}=1-y_1y_2 I need to show that the steady state solutions are y_1=\pm...

Finding the integrating factor (ODEs) [Solved] Working on this problem, I can't figure out why we take the derivative of \mu with respect to y, and what to do when our integrating factor is a function of both x and y. In the case below, it ended up being separable, but what can you do if it's...

I have learned Calculus (single and multi-variable) Ordinary Differential equations (upto 2nd order linear with Laplace transforms, including Dirac Delta functions and Fourier Series. I have not learned series solutions nor special functions which I see is the next step in this chapter)...

I don't understand what is happening in the following problem. What happens to ln when it moves to the RHS? Why are there two exponential functions on the RHS and why is e^c made to equal A? http://users.on.net/~rohanlal/mathproblemln.jpg

Homework Statement y"+3y'+2y= sin x y(0)=0 y'(0)=1 Evaluate y(0.1) Homework Equations Power Series Equation The Attempt at a Solution

Homework Statement Find all values of a for which all solutions of y''(x) + (a/x)y'(x) + (5/2)y(x) = 0 tend to zero as x tends 0+ and all values for which all solutions tend to zero as x tends to + Homework Equations The Attempt at a Solution I am not even sure where to being with this...

Homework Statement Solve the following problems using Laplace Transforms: y' - y = 2e^t, y_0 = 3 y'' + 4y' + 4y = e^{-2t}, y_0 = 0, y_0' = 4 y'' + y = sin(t), y_0 = 1, y_0' = 0 y'' + y = sin(t), y_0 = 1, y_0' = -\frac{1}{2} Homework Equations N/A The Attempt at...

Let's suppose I know every coefficients this script: and y1 alfa y2 v y3 A y4 T function dy=isaacsimply(s,y) dy = zeros(4,1) global ... dy(1)=(Cd_for*q_inf*h*(sin(y(1)))^2+... g*y(3)*(rho-rho_inf)*cos(y(1))... +E*U_inf*sin(y(3)))/... (-rho*y(3)*y(2)^2); %dalfa...

I am trying to model a packed bed distillation column for a binary liquid in Python. Unfortunately, when I set up my system, I end up with a system of coupled non-linear first order ODEs with boundary conditions at opposite ends (feed conditions and exit conditions), and I do not know how to...

Analytical Solution to this? -- linear system of ODES Hi All, It's been awhile since I've even attempted to solve something analytically, so before jumping back into the text. Does the following already have a common solution that I can find somewhere? Thanks, dx1/dt = A1 + B1x1...

infinite series solution for NON-linear ODEs? Is it possible to use the infinite series method (Frobenius) to obtain general solutions of non-linear ODE's, I want to try a second order equation. Any good references where I can see how that goes exactly?

here is a simplified version of my working equtions y''' = \frac{(y'' y+y' y) y + y'y''}{y' + y''} and 3 related boundary conditions, is there some hints to solve such equation numerically? ThX

Okay, I know that this is probably a simple question but I've always been good at doing the complicated things and bad at doing the easy things :D Here's what I've got: Find the general solution for the system of coupled ODEs. Determine kind and stability of the critical point. Sketch phase...

Hi, it is well known that a second order ODe can be transformed into a system of two ODEs through the transformation u=y', v= y. Is the other way round possible? I mean, I have a system of 2 ODEs and want to transform it into a sucession on higher order problems that can be solved one after...

Hello everybody! Here are two ODE 2nd order I tried to solve, but I failed :( r''[t] - k/(r[t])^2 = 0 xy''[x] = ay[x] + b Could anyone of you please help me? Thanks in advance :)

Homework Statement I'm trying to understand the Variation of Parameters in ODEs and I came up to this following expression which i cannot solve: {2\,{e}^{-t}{e}^{-3\,t}\choose {e}^{-t}{e}^{-3\,t}} \int {\,{e}^{t} {e}^{\,t}\choose {e}^{3t}{2e}^{-3\,t}} {10\,\cos \left( t \right)...

Homework Statement I have two questions: 1) If i have two first order ODE y(1) and y(2) (in terms of time), i know how to plot y(1) versus time and y(2) versus time but i don't know how to plot y(2) versus y(1) 2)I have two second order ODES X''=... and Z''=... to solve this, we make the...

Homework Statement I have two questions: 1) If i have two first order ODE y(1) and y(2) (in terms of time), i know how to plot y(1) versus time and y(2) versus time but i don't know how to plot y(2) versus y(1) 2)I have two second order ODES X''=... and Z''=... to solve this, we make the...

Anyone have much knowledge on the ODE solvers in matlab? I have an ODE and I want to specificy whether the input is time or the y value for the dy/dt problem.

Suppose I already have a solution u to a first order ODE. If I try to solve this ODE without initial conditions and I get another solution w, then it can be regarded as a function of an arbitrary constant: w=w(C). Is it true to say that u = w(C) for some C? If so, how do I find such a C?

Hi, I want to analyze a system of ODEs arising in biology of the form: x'=a1*x*z y'=b1*x + b2*y z'=c1 + c2*z + c3*y*z with x,y,z state variables and a1,b1,b2,c1,c2,c3 constant parameters. The difference to a linear system of diffs eqs. is that two state variables are multiplied...

Hi, Can anyone please tell me how to go about solving this system of coupled ODEs.? 1) (-)(lambda) + vH''' = -2HH' +(H')^2 - G^2 2) vG'' = 2H'G - 2G'H lambda and v are constants. And the boundary conditions given are H(0) = H(d) = 0 H'(0) = omega * ( c1 * H''(0) + c2 * H'''(0) )...