Nonhomogeneous Definition and 77 Threads

Homework Statement (D^3 - D^2 + D - 1)y = e^x and y(0) = 0, y'(0) = 1, y"(0) = 0 Homework Equations D = d/dx The Attempt at a Solution Factoring the left side of the equation gives : (D^2 + 1)(D - 1)y = e^x Which has roots of +/- i and 1. So y(c) = Ae^x + Bsin(x) +...

How do you solve the system z(t+1)=Az(t)+b where A is a 2x2 matrix and z(t+1), z(t), b are 2x1 matricies? I solved the homogeneous solution: z(t)=P(D^t)(P^-1)z(0) where D is the diagonal matrix of eigenvalues of A and P is the matrix of eigenvectors. I tried to solve the nonhomogeneous...

Homework Statement Find the general solution to the diff equation using undetermined coefficients y''-2y'-3y = 3te^-1 Homework Equations The Attempt at a Solution r^2 - 2r -3 = 0 r = -1, 3 so y = c1 e^-t + c2e^3t + yp since e^-t already exists as a solution, i have to...

This is a question from a book in which I can't figure out, but it has no solutions at the back. Find the general solution to the PDE: xy ux + y2 (uy) - y u = y - x I've learned methods such as change of variables and characteristic curves, but I'm not sure how I can apply them in this...

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...

y''-2y''-3y=3e^2t find the general solution I have tried Ate^t, Ate^2, Ate^3 none have worked they all leave extra variables that don't match up. is there another combination I could try?

Hey guys just asking for a bit of help to get me on the right track. I have the non homogeneous de 4y" + 4y' + y = 3*x*e^x, which also has some inital conditions y(0)=0 and y'(0)=0. but i only need help with getting the particular solution. Tried method of constant coefficients and it...

Homework Statement By using the method of undetermined coefficients,find the particular solution of y''+y'+y=(sin x)^2 Homework Equations i know how to determine the particular solution IF it is sin x. Ex: sin x ====> Asin x + B cos x (particular) but i wonder how to determine the...

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 So I'm trying to solve Evans - PDE 2.5 # 12... "Write down an explicit formula for a solution of u_t - \Delta u + cu=f with (x,t) \in R^n \times (0,\infty) u(x,0)=g(x)" Homework Equations The Attempt at a Solution I figure if I can a fundamental solution...

y'' - 3y' + 2y = et + t2 r = 1, 2 -> yc = c1et+c2e2t yp1 = Atet since Aet is a linear combination of our solution to yc. yp2 = At2+Bt+C y'p2 = 2At+B y''p2 = 2A via substitution we have 2A-3(2At+B)+2(At2+Bt+C) = t2 by isolating terms: 2At2 = t2 2A = 1 -> A = 1/2 -6At +...

Homework Statement y'' + 9y = 2x2e3x + 5 Homework Equations N/A The Attempt at a Solution I think the complementary solution yc = c1cos(3x) + c2sin(3x). If not for that little +5 at the end of the right hand side, I'm pretty sure I could solve it. But I don't know how to include it in my...

Hello. I am an engineering student and am having trouble trying to figure out how to solve this system of second order, nonhomogeneous equations. I know how to solve a single second order, nonhomo. equation and how to solve a system of first orders, but not this one. Any help would be greatly...

Trying to solve the ODE mx''(t) + bx'(t) + kx(t) = F(t) with m measured in Kg, b in Kg/s and Kg/s^2, F(t) in Kgm/s^2 and x(t) in m with initial conditions x(0) = 0 and x'(0) = 0, i got the following Green's function G(t,t') = \frac{1}{m\omega} e^{-\omega_1(t-t')}\sinh\left[\omega(t-t')\right]...

How would one obtain a Fourier Transform solution of a non homogeneous heat equation? I've arrived at a form that has \frac{\partial }{ \partial t }\hat u_c (\omega,t) + (\omega^2 + 1)\hat u_c (\omega,t) = -f(t) My professor gave us the hint to use an integrating factor, but I don't see...

I got this book from WILEY by Erwin Kreyszig. It tells how to solved homogenous cauchy equations. It also covers simple nonhomogenous equations. But it doesn't cover when we have nonhomogenous Cauchy equations like this one. x2y''-xy'+y=lnx How do I go about solving that equation? I substituted...

For the fun of it, my DE book threw in a couple of problems involving nonhomogenous second order DE's in the section I'm currently going through. Although I have solved for the complementary solution, any suggestions on how to find the particular solution? For example, the one I'm looking at...

Homework Statement Let A = \left( \begin{array}{l} \begin{array}{*{20}c} 0 & 1 & { - 1} \\ \end{array} \\ \begin{array}{*{20}c} 2 & 1 & 1 \\ \end{array} \\ \end{array} \right). Suppose that for some b in \mathbb{R}^2, p = \left( {\begin{array}{*{20}c} 1 \\ { - 1} \\ 1 \\...

I've got a nonhomogeneous BVP I'm trying to solve. Both my book and my professor tend to focus on the really hard cases and completely skipp over the easier ones like this, so I'm not really sure how to solve it. It's the heat equation in a disk (polar coordinates) with no angle dependence...

18.1 #33 Let L be a nonzero real # (a) Show that the boundary-value problem y''+vy=0, y(0)=0, y(L)=0, has only the trivial solution y=0 for the cases v=0 and v<0. I get (a), but I don't know how to do (b) (b) For the cases v>0, find the values of v for which this problem has a...

I was wondering if anyone could check my work on this to make sure I'm doing this right for finding a particular solution to y''' + 3y'' + 3y' + y = e^(-x) + 1 + x. First I split the problem into 2 halfs y_p1 and y_p2. y_p1 = Ce^(-x) -Ce^(-x) + 3Ce^(-x) - 3Ce^(-x) + Ce^(-x) = e^(-x)...

I got a particular solution y_p(x) that is different from what the book has. y'' + 9y = 2cos3x + 3sin3x Characteristic equation: r^2 + 9 = 0 (r+3i)(r-3i) = 0 y_c = c_1cos3x + c_2sin3x y_p = Acos3x + Bsin3x (not linearly independent, so I'll try another y_p) y_p = Axcos3x + Bxsin3x...

Let x = x1(t), y = y1(t) and x = x2(t), y = y2(t) be any two solutions of the linear nonhomogeneous system. x' = p_{11}(t)x + p_{12}(t)y + g_1(t) y' = p_{21}(t)x + p_{22}(t)y + g_2(t) Show that x = x1(t) - x2(t), y = y1(t) - y2(t) is a solution of the corresponding homogeneous sytem...

The following equation was derived from a RLC circuit: \frac{d^2}{dt^2} (V(t)) + 6 \frac{d}{dt} (V(t)) + 5V(t) = 40 Setting up the equation: s^2 +6s + 5 = 0 yields s = -1 and s = -5 Giving me the general equation: V(t) = k_{1}e^{-t} + k_{2}e^{-5t} But the general equation...

(d^2x/dt^2)+(w^2)x=Fsin(wt), x(0)=0,x'(0)=0 Hope that's readable. First part is second derivative of x with respect to t. w is a constant and F is a constant. I need to find a solution to this using method of undetermined coeffecients and I'm confused with all the different variables. Anyone...

Can anyone give me a hand with this, cause I'm stumped and can't remember exactly how to go about solving this. here's the eqn m[d^2x/dt^2 + wsubo^2 x] = F cos wt I'm supposed to show that x(t) = xsubo cos wt w is the incident freq wsubo is the resonant freq m is mass I'm stuck...

Hello, I am having trouble understanding how to solve second order nonhomogeneous linear differential equations. I know how to solve second order homogeneous linear differential equations. But I am not following in the lecture and in the text the method of variation of parameters to solve...