Undetermined coefficients Definition and 110 Threads

Hi all, I understand the basic concept of undetermined coefficients, but am a little lost when g(t) in the equation yll+p(t)yl+q(t)y=g(t) is a product of two functions. The specific problem I'm working on is as follows: yll-2yl-3y=-3te-t When I solve for the homogeneous set of solutions I...

Homework Statement I've been having problems with a number of these things, here's the first one: y'' -2y' -3y = -3te-t Homework Equations I know that the general solution will be y = yh + yp where yh is the general solution to the homogeneous equation, and yp is the particular...

Homework Statement Find a particular solution. 1. y'' +4y = 4 cos (2t) (for this problem, the instructions tell me that the forcing term is a solution of the associated homogeneous solution) 2. y'' + 16 y = 3 sin (4t) Homework Equations The Attempt at a Solution 1. I guess...

Hi, I've come across a problem in my differential equations book that I can't seem to be able to solve (it's not a homework problem, I'm just practicing): "Using matrix algebra techniques and the method of undetermined coefficients, find a general solution for x''(t) + y'(t) - x(t) +...

Ok, please view the attached image for the Question, and for the given solution. I need some help understanding the solution. I can get the Complimentary equation with no problems, I understand how to do that. However, some questions 1) Why do we first ignore the sin(3x) in our...

[PLAIN]http://www.undeclaredcomics.com/wp-content/uploads/2011/06/rsz_2011-06-06-everyone-gets-it-except-you.png

Homework Statement Decide whether or not the method of indetermined coefficients can be applied to find a particular solution of the given equation: The attempt at a solution I think the answer is yes, because the equation is of the form: a\ddot{y}+b\dot{y}+cy=F(t)where F(t) is the...

Homework Statement y" + y = 2/sin(x) solve for y Homework Equations I tried to use variation of parameters to solve this but I don't know how to check it. The Attempt at a Solution y = -2xcosx + (constant)cosx + 2ln(sin(x))sinx + (constant)sinx How do I do this using...

y''-2y'-3y=-3te^-t i know that that the general solution to this problem is yh = c1e^3t + c2e^-t i am having trouble figuring out what the particular solution is (yp) i keep getting the yp = 3/4te^-t , but wolfram alpha is telling me that the answer is something else. how do i get...

I'm working on undetermined coefficients for nonhomogeneous equations. I have an equation that is equal to 3xe^x. For an earlier one that was equal to e raised to 8x, I used Ae^8x; but on this one, obviously that won't work. I don't know what I should be looking at. I tried Axe^x but no dice...

Homework Statement Set up but do not solve for the appropriate particular solution yp for the differential equation y''+25y=2xsin(5x) using the Method of Undetermined Coefficients (primes indicate derivatives with respect to x). Homework Equations The Attempt at a Solution I first solved the...

Correct me if I'm wrong. :) I'm starting to learn basics of the ordinary differential equations, and I have some troubles understanding the concept and method as a whole. I understand when to use the method of undetermined coefficients (MUC) as opposed from variation of parameters. Suppose...

I have the problem "Find the particular solution of 4y''+4y'+y=3xex. What would be the assumed function y? Like would it be Ax ex?

y''+9y=sin(3t) I need to solve the above using the method of undetermined coefficients. I have already found the solution to y''+9y=0 is c1(Cos3t)+c2(sin3t). The problem is finding the particular solution. From class I am aware that the general form of the solution is...

Undetermined Coefficients, just a piece i need help with please In one of the last steps in trying to find the Coefficients of Yp (particular solution), I am supposed to set coefficients of similar terms equal to each other. Here's where i need help: i have A(e^x) + (-2B-2C+2F+E)sinx +...

Homework Statement Find a particular solution of y'' + 2y' + 5y = e^x * sin(x)Homework Equations The Attempt at a Solution Characteristic equation: r^2 + 2r + 5 = 0. Through quadratic formula, r1 = -1+2i and r2 = -1-2i, so my homogeneous equation is y_h = c1 * e^(-x) cos(2x) + c2 * e^(-x) *...

Homework Statement y''+y'=g(x) fundamental set of solns. of the homog. DE is: y1= 1 , y2= e^-x If g(x) = x^2 , yp1 = ____ Homework Equations The Attempt at a Solution I actually am looking at a key to an old test my teacher gave as a review for a test. The key has the...

Homework Statement Solve using Method of Undetermined Coefficients: y'' - 2y' + 3y = 15t - 8 The Attempt at a Solution First I used the characteristic equation to solve for the homogeneous solution to get: yh = C1e-t + C2e3t Great. Now I need to find the particular. I am...

Homework Statement y''' + y'' - 6y' = 36x Homework Equations y'' + y' - 6y =18x^2 The Attempt at a Solution I've integrated the third order D.E. to get a second order D.E. Solving the characteristic equation, to find a general solution, I get: y = c_1exp(-3x) + c_2exp(2x)...

Homework Statement y'' + 3y' + 2y = 24exp(-2x) Homework Equations y'' + 3y' + 2y = 24exp(-2x) The Attempt at a Solution I've solved the characteristic equation and am after the particular solution. I've let y_p = Aexp(-2x), y_p' = -2Axexp(-2x) and y_p'' = 4Axexp(-2x) When...

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 Problem #4 from here: http://www.math.washington.edu/~jtittelf/ExtraCredit.pdf Homework Equations ? The Attempt at a Solution There's only one example of using undetermined coefficients in my textbook. I'm not sure where to start. x = t2a + tb + c ? That's...

Homework Statement Derive a formula of the form \int\stackrel{b}{a}f(x)dx \approx c_{0}f(a)+c_{1}f(b)+c_{2}f'(a)+c_{3}f'(b) that is exact for polynomials of the highest degree possible. Apply a change of variable: y=x-a Homework Equations The Attempt at a Solution I don't get the "highest...

Homework Statement Given are the points (1,-4), (3,0), and (4,1). I am to usemethod of undetermined coefficients. Homework Equations Given these points I am to find a quadratic equation. The Attempt at a Solution Sorry! But I really do not have any clue. May anyone help me?

Homework Statement Find the unique solution to the differential equation y''+4y'−5y=−435sin(2t) satisfying the initial conditions y(0)=29 and y'(0)=47 The Attempt at a Solution So (I think) I found the correct general solution. I let y(t)=Acos(2t)+Bsin(2t) and eventually worked...

Homework Statement y''-49y=7cos(7x)+7+e^(7x) The Attempt at a Solution I have no idea how to solve this Differential equation. I could solve one that has y''-49y=one term, but I'm stumped with more than one. First, I get the homogeneous equation, y''-49y=0 and fine y_c, then use the...

I am working on a section on undetermined coefficients of a difference. I'm really trying to understand the material, but am struggling. y_{n+1}-2y_{n}=2 I got as far as saying for the homogenous equation y=c_{1}(-1)^{n}. I'm assuming the guess next would be A, but I'm confused. Maybe if...

Homework Statement y''-4y=60e4t y(0)=9 and y'(0)=2 Homework Equations none in particular The Attempt at a Solution First I solved for the auxiliary equation. r2-4r r(r-4) r=0, 4 So the general solution for the homogenous form is C1e0x+C2e4x where C1 and C2 are unknown coefficients to...

Find the solution of: y" + 3y' = 72sin(3t) + 36cos(3t) where y(0) = 6 and y'(0) = 9 I first found the solution to the homogeneous eq: the roots (R^2 + 3R = 0) are R = 0, -3 which gives the family of solutions: y = a(1) + be^(-3t) and y' = -3be^(-3t) using the initial conditions...

Homework Statement y'' - 5y' = 2x^3 - 4x^2 -x + 6 The Attempt at a Solution I first found the m's on the left hand side. They are 0 and 5. I then found the m's on the right hand side. They are 0, 0, 0, and 0. I then wrote my interim equation: y = C1 + C2e^5x + Ax^4 + Bx^3 +...

Homework Statement y'' + y = sin x + x*cos x Homework Equations The Attempt at a Solution i don't like undetermined coefficients. so far, for me, it's been so much trial and error, although i am getting a little faster at it. anyway, i didn't work out the homogeneous equation...

been working on these all week some help please.. 9) 3y''-6y'+30y= 15sinx+exp(x)tan(3x) 10) y''-2y'+y= 4x^2 -3+ Exp(x)/x[b]2. Homework Equations Variations of parame Method of undetermined coefficients thoughts: i think that you need to split the eqtuaion into 2 parts. Using variation of...

Homework Statement Obtain the Taylor series solution up to and including order 3 of the following non linear ode y'=x^2+\sin y,y(0)=\frac{\pi}{2} Homework Equations After substituting the power series form of sin(y) I get: y'=x^2+(y-\frac{y^3}{3!}+\frac{y^5}{5!}-\frac{y^7}{7!}...)...

Homework Statement y(4)-4y2=t2+et Determine the general solution Homework Equations The Attempt at a Solution So I worked it all out and got the correct answer. My question is that when we make the onsat that a particular solution will be in the form Y=At4+...how do we know it...

Homework Statement i have this problem y'' - y' - 2y= -6xe^{-x} Homework Equations this is the homogenous solution : y_{h}= c_{1} e^{-x} + c_{2} e^{2x} The Attempt at a Solution first i can do the problem but what is perplexing me is why of these two tentative...

Use of "method of undetermined coefficients" Hi all, Suppose I have a equation f(z+1) - f(z) = z^{1/2} , \forall z \geq 0 eq (1) then is it possible to solve this equation by the method of undetermined coefficients ? It is usually seen in textbooks that the forcing function is taken to be...

Homework Statement Find General Solution: y"+6y'+9y=e-3x-27x2 Homework Equations The Attempt at a Solution I know you have yh which is the general solution to the left side of the equation set to 0 and then fine the particular solution. When i try to find yp1 I get...

i solved homogenous but y"+y'+4y = 2sinh(T) is giving me trouble also have a hint sinh t = (e^t - e^-t)/2 also my "guess" was aE^t +Be^-t=Y maybe my guess was wrong?

Homework Statement So I'm doing a systems of DEs question with undetermined coefficients. After comparing coefficients, I have this: a+b=Ab+(1,0)T where a&b are vectors (2D) and A is the coefficient matrix: [2 -1] [3 -2] I know that 'a' is (1,1)T. I need to find b. I tried...

Undetermined Coefficients to solve. y'''-6y''=3-cosx So I set everything up, get my system & I get an answer of y=c1+c2x+c3e^(6x)-6/37cosx+1/37sinx the book has y=c1+c2x+c3e^(6x)-6/37cosx+1/37sinx-1/4x^2. So I'm not sure where the book gets the last term, any ideas?

NonHomogeneous Equations and Undetermined Coefficients Find the particular solution; y''-10y'+25y=-18e^(5t) here is my work yp(x)=-Ae^(5t) yp'(x)=-5Ae^(5t) yp''(x)=-25Ae^(5t) plug into equation [-25Ae^(5t)]-10[-5Ae^(5t)]+25[-Ae^(5t)... Now; I have 0=-18e^(5t) which doesn't...

Homework Statement Find the general solution of the given differential equation: y'' + 9y = (t^2)(e^3t) + 6 Homework Equations The Attempt at a Solution I want to first find a particular solution using the method of undetermined coefficients, but I'm not sure what I should...

How do I go about solving a DE using the method of undetermined coeficients in a question like for example; y''-4y'+4y=2e^2x I tried assuming the yp to be Ae^2x but when I plugged it into the DE I ended up with 0=2e^2x ??

Hi, When using the method of undetermined coefficients to solve 2y'' + y' = cos(2x) + 4x + 1 I did it term by term. I figured out the first yp1 for the cos(2x). I'm just not sure what to "guess" as to the form of the yp2 for 4x+1 Does anyone know what to use as the guess?

Given y'(t) + i*k*y(t) - i*g*x(t) = 0 What "form" does x(t) take?

Hi, new here, I am looking for some help on this homework problem. pretty sure you need to separate yp into 2 parts? anyways, use method of undetermined coeff. to solve y" + y = x*cos(x) - cos(x) thanks.

[SOLVED] (Methods)Parameters v Undetermined Coefficients Can anyone tell me why I would use one technique over the other? It seems as though undetermined Coef. is much easier to do but I suppose that comes with limitations?

Homework Statement Find solution for y'' + y' -2y = 2x with initial values of y(0) = 0, y'(0) = 1 Homework Equations I have found yc = c1*exp(-2x) + c2*exp(x), but finding yp is what I'm having trouble with... AND THEN I'm not so sure how to go about the initial value. The Attempt at...

Homework Statement tyʺ+yʹ=4t Homework Equations The Attempt at a Solution The problem that I am having with this problem is I've never been shown how to calculate the particular solution when there is an unknown (t) on the left hand side of the equation. If the problem were...

Greetings, Regarding the two procedures: undetermined coefficients and variation of parameters, can both procedures be used interchangeably - meaning they both solve (non-homogeneous linear equations)? Does one method work better in certain situations, if so which method is preferred when...