Ode Definition and 1000 Threads

Homework Statement Verify that y1(x) = 1 and y2(x) = x^.5 are solutions of the following y y'' + (y')^.5 = 0. Then show that c1 + c2 x^.5 is not in general a solution of this equation. Homework Equations The Attempt at a Solution I was able to show that both y1 and y2 are...

Hi all, I have an ODE with the form \frac{\mathrm{d}^{2}\phi}{\mathrm{d}x^{2}}+a\exp(b\phi)=0 B.C. \frac{\mathrm{d}\phi}{\mathrm{d}{x}}\right|_{x=0}=-c,\frac{\mathrm{d}\phi}{\mathrm{d}{x}}\right|_{x=L}=0 where a,b,c,L are all positive. I solved the problem with Maple using the dsolve...

Homework Statement It will be great if someone could show me some options: I need to prove the following: A particle of mass m is attracted toward a fixed point O (the origin) with a force proportional to its instantaneous distance from O raised to a positive integer power, i.e...

How can this equation be solved? \frac{dx}{dt}=ax(b-x)

Homework Statement Homework Equations (1) y\prime\prime+p(x)y\prime+q(x)y=g(x) (2) y\prime\prime+p(x)y\prime+q(x)y=0 If y1 and y2 are complimentary solutions of (2), then a particular solution of (1) is given by Yp = u1*y1 + u2*y2 The Attempt at a Solution Anyone have a good...

Title should read "Combining", is there anyway a moderator could alter that so the search function isn't messed up? Homework Statement The Attempt at a Solution I am familiar with both methods, however combining the two is foreign to me. Anyone have any suggestions for this ODE? My...

Homework Statement Find the first 6 terms of the power series expansion centered at 0 for the general solution for y -xy'=0. Then find the coefficient of the x38 term. Homework Equations General solution is of the form: y=a0+a1x+a2x2+a3x3+a4x4+a5x5+... If you factor out the ao and...

Homework Statement Finding the general solution of y'= (2y^2)/e^x and the particular given that y(0) = 0 The Attempt at a Solution I separate variables etc. to get y = -1/(2c-2e^(-x)) where c is the constant. The problem then is obtaining the particular solution. If I substitute y and...

A model of tank fluid temperature (fixed mass inside) based on the mixing of two streams, one hot and one cold, each with fixed temperature, the hot one a fixed flowrate and the cold one an oscillatory flowrate can be expressed as: du/dt + [c1 + c2*(1+cos(t))]*u = c1 The solution can be...

Hi, could someone show me the steps to solve the equation d^2y/dx^2 = -ky for the solution A*exp(i*sqrt(k)*x) + B*exp(-i*sqrt(k)*x) ? I am trying to solve the time independent Schrodinger equation for a free particle, and the above question is of the same form. Wikipedia says it...

Homework Statement Solve the following ODE: x^3y'-2y+2x=0 Homework Equations The solution should be a function continuous in R \ {0}. The Attempt at a Solution Pretty helpless about this one.

second order nonlinear ODE -- not autonomous This equation has arisen from a steady state problem of diffusion with nonlinear reaction: (dependent var=c; independent variable=x) c'' = ko + k1 c + k2 c^2 + k3 c x ko, etc are constants. I can obtain a solution if I drop the last term...

Homework Statement Solve the following equation f'' - 3f' + 2f = 3 For f(0) = 0,\ and\ f'(0) = 1 Homework Equations None. The Attempt at a Solution Ok, so, I know how to solve inhomogeneous ODEs when it's on this form af'' + bf' + cf = g Where g is a given function. But how do I...

y[1+(y')^2] = k First solve for dx in terms of y and dy, an then use the substitution y = ksin2(θ) to obtain a parametric form of the solution. The curve turns out to be a cycloid. My attempt: (y')^2 = k/y-1 dy/dx = sqrt(k/y-1) dx = dy/[sqrt(k/y-1)] then substitute y =...

Homework Statement You are given that two solutions to the homogeneous Euler-Cauchy equation x^2 \frac{d^2}{dx^2}y(x) - 5x \frac{d}{dx} y(x) + 5y(x) = 0 y1=x, y2=x^5 y''-\frac{5}{x}y'+\frac{5}{x^2}y=-\frac{49}{x^4} changing the equation to standard form use variation of parameters to find a...

Homework Statement There are two storage rooms, (A) and (B) connected by a single doorway. Only room (B) has an outward vent, so all air exiting the rooms does so through this vent in room (B). The ventilator you will install drives outside air (78% nitrogen) at a certain flow rate through a...

I'm a Physics/Math major- and am setting up my degree plan I've posted a similar thread before but now I only have one math elective left (and a boatload of choices, all of which sound interesting) I've narrowed it down to either: Integral Calculus, Topology, or Theory of Ordinary...

Homework Statement y'' + 9y' = cot(3t) Homework Equations The Attempt at a Solution This is a linear second order ODE where y(t) and that's what I'm solving for. Can this be solved via an integrating factor or does the cot(3t) part make that invalid? Any help is appreciated.

Homework Statement y'' + ty' - y = 0 plugging in the known Laplace formuals i get this... [s^2Y(s) - sy(0) - y'(0)] + [-sY'(s) - Y(s)] - Y(s) = 0 Homework Equations y(0) = 0 y'(0) = 3 The Attempt at a Solution simplying to a linear first order DE -sY'(s) + (s^2-2)Y(s) = 3...

Question: find the general solution of xX' = aX i know it's kinda simple ode.. but, i just don't know y i can't get the correct answer.. solution.. xX' = aX x dX/dx = aX d/dx X = aX/x X = ∫aX/x dx X = aX ln |x| + C the general solution is Ax^a problem : i can't get the...

Homework Statement A college graduate borrows $100,000 at an interest rate of 9% to buy a house. The college graduate plans to make payments at a monthly rate of 800(1+t/120), t is the number of months since the loan was made. Assuming this payment schedule can be maintained, when will the loan...

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...

Is it possible to form a new solution of a second order ODE by multiplying it by an exponential factor?

Homework Statement The motion of various shaped objects that bob in a pool of water can be modeled by a second order differential equation derived from F = ma. The forces acting on the object are: 1)force due to gravity, 2)a frictional force by water, 3)and a buoyant force based on...

i have found the general solution which is, u(x)= (C1 + C2x)e^ax + (1/2a)[tex]\int f(x-y) e^\left|y\right| dy is this correct?? now, i just want your help to guide me for justifying f(x)=x^5... is that wrong if i solve the integration and just substitute the integral which is the...

Hello, My question seems to be simple. I would like to numerically solve the following first order ODE to obtain v(x): v'(x) = b.[v(x) - f(x)] , given boundary condition v(+infinity) = 0 [b is a known constant] The problem is that f(x) is not known explicitly (f(x) is sampled at a...

ok well I'm pretty much home and dry in this problem the aim of this problem is to get the general solution for the ode below.. 2u'' - xu' + u = 0 = g(x) i started to solve it by rearranging the equation.. 2u'' + u = xu' apply Fourier transform.. 2F(u'') + u^ = g^ (-2k^2)u^ + u^...

Homework Statement Solve: (1-\frac{x}{y})dx + (2xy + \frac{x}{y} + \frac{x^2}{y^2})dy = 0 The Attempt at a Solution No idea what strategy to use here. Tried using an integrating factor, but no success. A lot of x/y in here makes me think I need to use a substitution, but there's also...

Homework Statement Solve: y'' -y' e^{y'^2-y^2} = 0 y(0) = 1 y'(0) = 0 Homework Equations The Attempt at a Solution No idea how to use it. If I use the substituion y' = p, and y'' = p'p I need to integrate e^{y^2} which is unintegratable. What should I do?

Homework Statement Using laplace transform, solve: y'' - y = \frac{x^2-3x+2}{|x^2-3x+2|} y(0)=y'(0)=0 Homework Equations The Attempt at a Solution Just to know if I'm on the right path - Since the quadratic has 2 roots, at 1 and at 2, the entire thing can be equal to...

Homework Statement yy'' = (y')2 - (y')3 Homework Equations The Attempt at a Solution y' = p(y) y'' - p'p yp' = p - p2 dp/p + dp/(1-p) = dy/y ln|p|+ln|1-p| = ln|y|+c p-p2 = cy y' - y'2 = cy now what? how do I solve for y? I think I'm missing some stupid...

hey there.. i've got unsolved question here.. Question: Solve the initial value problem. 2yy’ = x / √x^2 – 16 ; y(5) = 2 2yy’ = x / √x^2 – 16 2y dy/dx = x / √x^2 – 16 ∫2y dy = ∫ x / √x^2 – 16 dx y^2 = √x^2 – 16 y = (√x^2 – 16)^1/2 my answer was wrong. the answer is y = ((√x^2 –...

[b] Find the general solution of the following ODE: dx/dt = 3x^(2) cos t [b] Make x the subject of the solution. [b] Heres my solution, is this correct? dx/dt = 3x^(2) cos t dx/3x^(2) = cos t dt Integrating both sides gives: ln (3x^(2)) = sin t + C 3x^(2) =...

Homework Statement Find the solution to the two-point boundary value problem u'' + 4u' + exu = sin(8x) with u(-1) = u(1) = 0. Homework Equations The Attempt at a Solution I haven't taken an ODE course in years but I need to verify that my numerical solution to the ODE is accurate to the...

Find y(t) from the following first order ODE Homework Equations y' = 20SQRT10 x (1-e^(t/SQRT10))/(1+e(t/SQRT10)) The Attempt at a Solution I know I must integrate to gain the solution but am having problems getting started please any help greatly appreciated!

Homework Statement Find the general solution of y'=\sqrt{2x-y} Homework Equations -- The Attempt at a Solution I've tried approaching this equation through several methods, but I can't separate the variables, I can't make it fit the pattern for linear, I can't make it fit the...

From PDE to ODE ?! + research Homework Statement In the attached research, What are the steps that we work to transform the equation (1) to (8) Homework Equations (1) and (8) The Attempt at a Solution I know that they used similarity transformations but I do not know how to do...

So I have never solved a second order NON LINEAR ode before, but my current project has thrown one at me. I am going to use MATLAB to solve it when I have it in the correct state, but at the mo, I can't get it to that... Its three coulped equations, in terms of x,theta and x2. They are in a...

Note: this has been edited to fix a typo. Homework Statement The problem is to find the maximum solution on all of R of the differential equation dy/dt = t * y^(1/3) subject to the initial-value conditoin y(1) = -1.Homework EquationsThe Attempt at a Solution This equation is not subject to...

hi there, I'm trying to plot r against \phi by solving the following ODEs using runge-kutta. The problem I'm having is with the square root. How do I know when it will be positive and when it will be negative? If this is a simple question I apologise I'm not that great with the maths :). E and...

I am a senior in mathematics studying graduate point-set topoology atm. I am thinking I want to study differential topology in graduate school and maybe apply it to problems in cosmology. Do I need to take more ODE and PDE? I took intro to diff eq- the one that all engineering undergrads take...

In class, my teacher gave the following equations as examples of linear and nonlinear ODE. In the first equation, there are x's in front of some of the y's yet it is linear. In the second equation, there is an x in front of y^2 yet it is nonlinear - why? Also, why is the final equation...

If we assume air resistance is negligible, the only force acting on a body is -Mg where g is the acceleration due to gravity ( negative because acting downwards). F = Ma becomes : -Mg = M y'' which implies y[B]''=-g Question asks find the general solution for y. Homework Equations...

Hi, I'm nearly finished with calc III ala Thomas Calculus. I'm really just clearing up any stray concepts and was thinking of getting the Dover book Ordinary Differential Equations by Tenenbaum/Pollard. I'm wondering would the book be a giant leap...

Homework Statement A point in a mechanics problem where I have to solve the ODE (dS/dx)^2 + mw^2x^2 = a where m,w^2 are constants Homework Equations The Attempt at a Solution Hi everyone, We haven't actually covered how to solve these in my ODEs class yet (obviously my...

Hello, I was wondering if anyone could shed some light upon solving this: s(x)'' = (a b s(x)) / ||s(x)||^3 Where s is a n dimensional vector, || || is operation finding the magnitude and a and b are constants. Is this solveable or will I have to use alternative numerical methods?

Hi all, I've been staring at this for much to long: y''+2y=6x+4 what were going over now is homogeneous and inhomogeneous differential equations but i can't seem to think of a method for solving this one other then by inspection. Thank you very much for your help.

Out of boredom* I derived some simplified equations to describe the dynamics of a pneumatic gun. These equations are extremely simplified, but they should provide some insight into the system that my numerical models can't. This system had one non-linear equation that could be rewritten as the...

Find k: 20\frac{d^2x}{dt^2} + \frac{dx}{dt} + kx = 0 when t = 0 - x = 1 - dx/dt = 1 My attempt at this in maxima: (%i1) 20*'diff( 'diff(x, t), t) + 'diff(x, t) + k*x = 0; 2 d x dx (%o1) 20 --- + -- +...

Homework Statement A cell of some bacteria divides into two cells every 40 minutes. The initial population is 2 bacteria. a)Find the size of the population after t hours b) Find the size of the population after 6 hours. c) When will the population reach 12? Homework Equations...