# nonhomogeneous

1. ### non-homogeneous recurrence problem

Hello everyone, I have this problem $a_n + a_{n-1} + 6a_{n-2} = 5n(-1)^n + 2^n$ This is the given solution: a_n = (\sqrt{6})^n(C_1\cdot \sin\phi n + C_2\cdot \cos\phi n) + \frac{1}{3} \cdot 2^n + \left(\frac{5}{6}\cdot n + \frac{55}{36}\right)(-1)^n I used the discriminant to find the zeros...
2. ### General solutions for non-homogeneous diff eq

Hey guys ! I have some troubles with these types of differential equations. I have to find the general solution of this eq : y''-4y'+5y=e^(2s) I have found the general solution of the homogeneous part of this eq. Yh= e^(2s) * ( c1* cos s - c2 * sin s ) I hope it's correct. Well, my...
3. ### solving a multi-dimensional non-homogeneous transient PDE

Hi, in the context of my graduation project I want to solve a 2D, transient hon-homogeneous conduction problem with convective boundary conditions in cylindrical coordinates (see file attached ) according to an online source: "This problem can be decomposed into a set of steady state...
4. ### Non-homogeneous Equation; killing me!

Hey guys, This is my first post here! Because I really stuck with this Non-homogeneous Eq. y''-y'-2y=3e^(-t) When I tried to solve it to find A, I always end up with: 2Ae^(-t)-2Ae^(-t) which gives ZERO=3e^(-t) So, I couldn't solve for A since there is no A! Did I miss something? Plz...
5. ### 2 Order Linear Nonhomogeneous ODE problem

I have a problem working out the particular solution for this ODE: y''-y'=4cosh(x) yh = Ae^0x + Be^x = A + Be^x yp => cosh(x) = 0.5(e^x + e^-x) 4cosh(x) = 2(e^x + e^-x) yp = Cxe^x + Dxe^-x yp' = Cxe^x+Ce^x - Dxe^-x + De^-x yp'' = Cxe^x + Ce^x + Ce^x + Dxe^-x - De^-x - De^-x...
6. ### Non-homogeneous Differential Equations

I am trying to solve the following: y'' - 3y' +2y = e^2x This is my attempt so far: r^2 - 3r +2 = 0 (r-2)(r-1)= 0 Let's try solution of Y(x) = Ae^2x 4Ae^2x - 6Ae^2x + 2Ae^2x = e^2x 0 = e^2x I don't seem to get be able to get a coefficient for A, as everything on the left-hand side cancels...

Hi! My differential equations professor is one of those people who is really just entirely too smart to be teaching, and with finals coming up, I'm starting to panic. I have 3 problems I'd like to know how to do, and neither the course's 1960s textbook nor Differential Equations for Dummies has...
8. ### Nonhomogeneous Linear Systems - Imaginary terms

Hey all, The question is as follows: x'=\begin{pmatrix} 2 & 1\\ -5 & -2 \end{pmatrix}x + \binom{-cos(t)}{sin(t)} I have solved a similar question with real eigenvaluesfor the A matrix using the following general term y=(T^{-1}AT)y+T^{-1}g(t), where g(t) regards the\binom{-cos(t)}{sin(t)}. I...
9. ### General Solution of the non-homogeneous differentia equation

Given the function y''+9y=9(sec(3x))^2, 0<x<(pi/6), find its general solution. I know that the solution is of the following form: y = c1y1 + c2y2+Y, where Y is -y1u1+y2u2. My main problem is finding following integrals: u1 = integral of -9xsin(3x)/(cos(3x))^2 u 2= integral integral of...
10. ### y''-y'=xe^x non-homogeneous linear equations

I've read some explanations on the internet about this question, but I still don't understand what is done with y_{p}. An "extra" x appears in the calculations, I'm not sure why. We're only studying the Method of Undetermined Coefficients, the Method of Variation of Parameters will not be...
11. ### help need for finding non-homogeneous solution

Numerical ODE help? Hello friends, I am new to this forum and I need some help in the following integration -------------------------------------------------------------------------. The governing equation x^2*y''+x*y'-x^2*q^2*y = ln(x). how to find non-homogeneous solution??? Maple gives...
12. ### Laplace Transformation of Second order Non-homogeneous DE

The differential equation is y"+y=t+cos(t) Initial conditions are y(2pi)=0 and y'(2pi)=0 I have completed this one all the way up to the part where you have to use partial fractions. I seem to be having trouble with partial fractions and the equating the coefficients method. I need to get...
13. ### find particular solution of non-homogeneous

Find by inspection particular solutions of 2 non-homogeneous equations y'' + 2y = 4 and y'' + 2y = 6x. I'm not sure what it means "by inspection." A method we used in lecture was to 'guess' that y_p = A_2 * x^2 + A_1 * x + A_0. So then I take it's first, second and third derivatives in order to...
14. ### differential equations - nonhomogeneous

Let L_y = y'' + py' + qy. Suppose y_1 and y_2 are two functions such that Ly_1 = f(x) and Ly_2 = g(x). Show that their sum y = y_1 + y_2 satisfies the math equation L_y = f(x) + g(x). I don't see anything showing that letter L in the section in the book, and I have a little bit of notes from...