Ode Definition and 1000 Threads

Okay, good, so y' = 3y is an autonomous ODE, while y'(t) = 3y(t) is not autonomous?? Seems like a contradiction in terms. Differentiation of a function with respect to a variable on which it doesn't depend, i.e. one which doesn't denote its argument, is meaningless. I might as well...

Homework Statement I'm trying to solve a second order ODE for y(x) to show that the solution is y(x)=sin(x)/x. We've been told to use the substitution y(x)=h(x)/x. I've got to the stage of solving for h(x), arriving at h''(x)=-x. Using the general solution, h(x)=A sin(x) + B cos(x) and...

Equations: (d^2r/dt^2) - r*(dθ/dt)^2 = -10/(r^2) and r^2*(dθ/dt)=1 How would I get three 1st order ODE's from this?

hi i am trying to solve second order ODE in MATLAB but when i write my scribt and call into the command window using ode45 i get input argument "a" is undefined i have spent so much time trying to figure out what the problem is but unsuccessful. the function is as follows function...

We are doing mass spring problems that stem from second order ODE's. I think my lack of linear algebra is hurting me once again in this section so any help would be greatly appreciated. We are using a stiffness matrix of K = [ -(k1+k2), k2 (row 2) k2, -(k2+k3)] Our first problem has the...

Homework Statement I'm given two equations first (d^2)*r/dt^2 - r((d*theta/dt)^2)= (-A)/r^2 --- this is a non linear second order differential equation second (r^2)*((d*theta)/dt)=B B and A are...

I'm curious how many people have taken a calculus course that invokes vectors and/or linear algebra before starting ODE? I did neither, as my school did not require it, and the tail end of ODE is excruciating because we are hitting on vectors and topics from LA that I do not have. So in...

Hi, All: I am taking a financial maths course and I encounter the following ODE: dy/dx = x+ x^2*y+x^3*y^2 I have tried many methods but cannot solve it. Can anyone help me? Thanks.

Homework Statement If b =\sigma^2 > 0 (which implies b is real), then the general solution is Ce^(i\sigmax) + De^(-i\sigmax) = Esin(\sigmax) + Fcos(\sigmax) = Gcos(\sigmax + H). Homework Equations N/A The Attempt at a Solution So I know how to get the first two forms of the...

3rd order homogeneous Linear ODE matrix transformation---how to write the answer Homework Statement Transform this 3rd order homogeneous linear ODE with constant coefficients using matrix notation. y'''+7y''+6y'+3y=0 Homework Equations The Attempt at a Solution My answer is x'=AX...

Homework Statement Transform this 3rd order homogeneous linear ODE with constant coefficients using matrix notation. y'''+7y''+6y'+3y=0 Homework Equations The Attempt at a Solution I can't find anything useful to start with on this one. I need some with starting this one, I've...

Homework Statement 22e^{2t}=y''+8y'-9y Homework Equations The Attempt at a Solution The directly previous question to this was the same but homogeneous, i.e. the 22e^(2t) was replaced with a 0. So I know the general solution to the homogeneous ode is C_1e^t+C_2e^{-9t} I know that r(x)=...

We're given the ODE xy''+y'+xy=0 and told that y=\int_0^{\pi} e^{ix\cos{t}}dt is one solution and it asks to find a second solution in the form of an integral for x>0. I'm not sure how to do this, I don't think they mean the second solution derived from the Wronskian as that just wouldn't "look...

Homework Statement I have the following ODE: \frac{d(f^2g)}{dx} = \frac{b}{fg}\qquad(1) Where b is a known constant, f is an unknown function of x that I am seeking, and g is a known function of x. Now, my next step was to actually plug in my known function of g(x), carry out the...

Homework Statement x^2 y''+2xy'-12y=0,y_1=x^3 y''+(2y')/x-12y/x^2 =0 Homework Equations The Attempt at a Solution y=uy_1=ux y'=u' x+u y''=u'' x+2u' subbing that in instead of y,y',y'' u'' x+2u'+2(u'x+u)/x+12(ux)/x^2 =0 now my book says to reduce the...

Homework Statement Homework Equations The Attempt at a Solution For part i) I got the answer 1/((jw)^2 + 5jw +6) For part ii) I first consider input to be a unit impulse Thus, Y(w)=H(w)F(w) and F(w)=1 yI(t)=-1/2pi integrate from -infinity to infinity (e^jwt)/(w^2 - 5jw -...

Hi all! I'm trying to solve the following system of ODE's, but somewhat unsuccessful... \dot \vec x = [-i\omega(t)\sigma_z - \nu(t)\sigma_y]\vec x with sigma_i the Pauli matrices and w(t) and v(t) well-behaved functions of t (actually I also have that w = 1+v). Nevertheless, v(t+T) =...

Homework Statement 22e^{2t}=y''+8y'-95 Homework Equations The Attempt at a Solution I've been reading a textbook on this and think that I should use "method of undetermined coefficients" I know r(x)=ke^{\gamma*x} so y_p(x)=Ce^{\gamma*x} The trouble is after reading the entire chapter I...

Homework Statement I have solved this by hand but we are also required to get Mathematica to spit out a solution and I need some help. (2xy-5)dx+(x^2+y^2)dy=0 , y(3)=1 Homework Equations The Attempt at a Solution I know the command is DSolve but I don't know how to put in dx...

Homework Statement x^3y'+xy=x, y(1)=2 Homework Equations The Attempt at a Solution I'm having trouble starting this because it doesn't fit any form I'm familiar with because of the x^3 in front of the y'. Can someone give me some pointers to get started..

Homework Statement (2x+y^2) dx +4xy dy=0,y(1)=1 Homework Equations The Attempt at a Solution I'm having trouble finding the correct integrating factor, been playing with it for an hour and have made NO progress so need help. \delta P/\delta y=2y \delta Q/\delta x=4y...

Homework Statement Solve y'=x^2+y^2 with initial condition y(0)=1. Homework Equations This is a first order ODE. The Attempt at a Solution I have tried separable variable, exact, and homogeneous and non-homogeneous, but none of them work. It's neither linear nor Bernoulli...

Homework Statement A particular solution of y'' + 4y = tanx Answer choices are: (a) 1/2*cos(2x)ln|sec(2x)+tan(2x)| (b) -1/2*cos(2x)ln|sec(2x)+tan(2x)| (c) 1/2*sin(2x)(ln*cos(x)+x*sec(2x)) (d) 1/2*sin(2x)(ln*cos(x)-x*sec(2x)) (e) none of the above Homework Equations The...

I am working on a problem requiring variation of parameters. When I calculated the wronskian, I got an answer, which differed from the book only by a "-" (mine was -, the book's was +). So I switched my functions for y1 and y2 and got the answer the book had. Is there a standard for which...

Nonlinear ODE, Howto attack... Hi, I've got a general nonlinear ODE equation that I have been solving in various situations, and I needed to make an approximate correction to -- but after the correction, an analytical solution to the new form evades me... So I am studying it, but my math...

ODE solutions :( hey guys, I am attempting to prove this: Verify that y is a solution of the ODE. Determine from y the particular solution satisfying the given initial condition. y' = 1 + 36y^2 , y = (1/6)tan(6x+c) y(0) = 0 It can be seen that it is a solution I then...

Hi, I have the differential equation \left(\frac{df}{dr}\right)^2-\frac{1}{r-1}\left(1+\frac{1}{4r^3}\right)=0, does anyone know how to attack this? (I'm led to believe this is only possible if r>1, not sure why not r<1, although I can see it does blow up at r=1) thanks

Hi, could anyone give me a hint on what method to use to solve this ODE: v''+(2/t)v'+(b)v=0, b is a constant and v=v(t). Most of my ODE training resolves around how to solve the above equation with constant coefficients. AND all of my reference books say that "the nonconstant case is...

Homework Statement solve x''(t)+w2x(t)=-gsin(a) with x(0)'=0 x(0)=-gsin(a)/w2 Homework Equations The Attempt at a Solution let x=Acoswt+Bsinwt+C x'=0 so B=0 x=Acoswt+C c=-gsina/w2 t=0, x=A-gsina/w2 but x(0)=-gsin(a)/w2 so A=0, and you get x is a constant, which...

Homework Statement The set of solutions of an ODE of the form y''+by'+cy=0 forms a vector space. To convince yourself of that, prove that axioms 1,4,5 and 9 of the definition of a vector space hold for this set of solutions. (You may want to check the others as well, but no need to present...

Homework Statement Ive been told to perform 2-3 Picard Iterations on the following problem Homework Equations y'' = 6y^2 With initial conditions: y(0) = 0 y'(0)= -2 The Attempt at a Solution In class we've gone through how to perform picard iterations and it has been easy so far...

Homework Statement What is the value of a such that the solution of the initial-value problem satisfies limx->infinity y(x) = 0? y''+y'=e^(-x), y(0)=1, y'(0)=a Homework Equations The Attempt at a Solution Not sure what to do with the missing y term... yp=Ae^(-x), y'p=-A^(-x), y''p=A^(-x)...

Homework Statement Suppose the Wronskian of W(y1, y2) [0] = 1 y1, y2 are solutions to the differential: y'' + e^xy'+ tanx = 0 Find W(y1, y2)[1] ? The Attempt at a Solution So I'm thinking of using Abel's theorem, where p(x) = e^x W(y1, y2)(0) = = c e^{\int{- e^t dt}} So, 1 = ce^{e^{-t}} But...

Hiii, In my research i encountared with following 3rd order ODE: d^3y/dx^3 = (1-y)/y^3. my B.C. are: at x = 50 y=1(dirichlet B.C.) ; dy/dx=0 ( numan B.C.) and d^2y/dx^2=0. i need to integrate from x=0:50. I tried ode45 but it gives same result as B.C. throughout the range...

Homework Statement Latex takes me forever so I'm going to take a picture Homework Equations The Attempt at a Solution I'm having issues with integrating functions. There seems to be this (x-x0) term that crops up everywhere. Last time it was (t - tau). It's always (variable -...

Homework Statement y''-3y'+2y=t e^{2t}+sin(5t) Homework Equations The Attempt at a Solution I can get as far as this: y_h(t)=c_1 e^{2t} + c_2 e^{t} y_p(t)=At e^{2t} + B e^{2t} + C sin(5t) + D cos(5t) My professor says we multiply At e^{2t} + B e^{2t} by t to give At^2...

Alright. So I have dy/dx = -1-y2. I want to take the second derivative to get some information about the concavity of the solution, but I can't wrap my head around what's really going on. What I think I know: I have an ODE that is dependent on the dependent variable, so my solution will only...

solve dy/dx = (x+y)^2 , y(0)=1 i let w = (x+y) and got the above equation rearranged to dw/dx - 1=w^2 after solving for C i got y=tan(x-pi/4) - x just wanted to check my answer

Homework Statement xy'-(x+2)y=-2x2-2x Homework Equations The Attempt at a Solution I'm clueless as to how to solve this as I'm only experienced in using the power series method with homogenous ODE's. Even if I make this homogenous, I don't know what to do with the x-variables that are not...

I need to solve the following ODE \frac{dy}{dx}=\frac{x(1-x^2)+ky^2}{y} I don't know what is the correct method to use though. Any help would be brilliant, thanks.

First, I looked for a MATLAB forum here but didn't see one so if there is and I missed it let me know for future posts I have a few more questions. Second, this isn't ode related but plays a small part in the next, longer question. This is two parts: I have an i7 980x w/12GB of RAM 2 gtx 295s...

Homework Statement Find a general solution. Homework Equations 2x\frac{dy}{dx}+y^{3}e^{-2x}=2xy The Attempt at a Solution Looks like a Bernoulli equation to me, after some algebra: \frac{dy}{dx}+\frac{y^{3}}{2xe^{2x}}=y \frac{dy}{dx}+\frac{y}{2xe^{2x}}=y^{-1} so with...

I would appreciate any advice on the following ODE substitution question: xy' = y + (x^2 + y^2)^.5 Dividing thru by x and using the usual y/x substitution, I get: y' = v + (1 + v^2)^.5 but I don't know if that is right or how to integrate the left side. The book has the answer of y + (x^2 +...

I have the following logistics problem that I am stuck about halfway thru: The time rate of change of a rabbit population P is proportional to the square root of P. At time t=0 (months) the population numbers 100 rabbits and is increasing at the rate of 20 rabbits per month. How many rabbits...

So I have the following Bernoulli ODE: x^2*y' + 2xy = 5y^3 I use an integrating factor of x^-4, my n value is 3. I am okay until I get to the very end, where I get y^-2 = (2+Cx^5)/x; the book shows y^2 = x/(2+Cx^5). Am I must missing an algebra step or did I make a mistake somewhere within?

Homework Statement Solve ODE of form y''+(2/x)y'=C*(e^y) where C is a constant Homework Equations The Attempt at a Solution I don't really see how to approach this one, so a point in the right direction would be great. Thanks,

Homework Statement Find a general solutionHomework Equations (x+y)\frac{dy}{dx} = x-y The Attempt at a Solution \frac{dy}{dx} = \frac{x-y}{x+y} let v=y/x y=xv \frac{dy}{dx} = v+x\frac{dv}{dx} now, v+x\frac{dv}{dx} = \frac{x-xv}{x+xv} = \frac{1-v}{1+v} = \frac{1}{1+v} -...

I know that the rate of change with time of a population is proportional to the square root of t. T=0 is y = 100. Population increases at rate of 20 per month. I started out by trying to do dy/dt = p^.5. I am used to the population problems where I use y=Ce^(rt) but am having trouble...

Tank w/ 100 gal pure water. At time = 0, sugar/water mixture with .2 lbs of sugar per gallon enters at 3 gal/ minute. Drain opened at bottom allows sugar solution to leave at 3 gal per minute. Perfect (lol) mixing occurs. I show the following: Rate in: .2 x 3 = .6 Rate out: x/100 Volume: 100...

dy/dx = (2/pi^(1/2))e^(-(x^2)) eq 1.17 My book makes a statement about the symmetry of the family of solutions to this diff eq I don't quite understand. "Symmetry. If we replace x with -x on both sides of 1.17, the right hand side is unchanged but the left hand side changes signs. So...