1. S

    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. N

    Homogenous stress/strain

    Hi all, Any help would be appreciated. A fibre-reinforced composite has 25% volume of carbon fibres with a modulus of elasticity of 150.0 GPa. The remaining matrix material is polyester resin with a modulus of elasticity of 3.10 GPa. Use the homogeneous strain (parallel) model, to...
  3. S

    Homogenous Differential Equation

    Please help me solve this differential equation xy'=√(x^2+y^2 ) I recognize this as homogenous differential equation of order 2.After substitution I get du/(sqrt(1+u)-u) = dx/x. How to solve this further. Please help. Got stuck while solving from GF Simmons
  4. D

    Non Homogenous Differential Equation.

    y''+y'=4x What I do: 1) y''+y'=0 I find solutions: x1 = 0 x2 = -1 2) I need to find another part of the answer. y* = x*(e^ax)*Q(x) The problem is, I don't know what is that last Q(x)? Is it that 4x function?
  5. szz

    Doubt with Homogenous Differential Equation

    Hi, I have a doubt with a Homogenous Differential Equation. This is an exercice I have found in a textbook, just the solution is shown (not its development). I would like to confirm if my development is right. HDE: xy^3\,\text{d}x = {x^4 + y^4}\,\text{d}x I proceed as follows...
  6. B

    Homogenous system problem

    Hello. As a new student, I just recently began learning about Linear Algebra. We have used the Gaussian Elimination on matrices, and are now moving on to linear systems. I have a problem, among many, to solve before monday 0600, and it bugs me quite a bit. It's relatively simple. You are given...
  7. R

    homogenous coordinates- explain please

    Can someone please explain to me how do we get the following homogenous coordinates of the equilateral triangle (its vertices) . In case k=\mathbb{Z}_{2} The base has (1:0:0) and (0:1:0) and the vertex (0:0:1) How do we get it? Why for example the origin in Cartesian plane is represented by...
  8. N

    Homogenous system with more variables than equations

    Did I solve this correctly? Solve the system. 3u - v + w -5x - y = 0 6u - 2v + 2w - 9x + y = 0 -9u + 3v - 3w + 11x -y = 0 Augmented matrix: \left[ \begin{array}{cccc} 3 & -1 & 1 & -5 & -1 & 0 \\ 6 & -2 & 2 & -9 & 1 & 0 \\ -9 & 3 & -3 & 11 & -1 & 0 \end{array} \right] = \left[...
  9. M

    Proof of homogenous

    How should I prove this problem: "Prove that the set of all solutions x of the linear systems Ax = b forms a subspace if and only if the system is homogenous." I proved it directly, will this attempt suffice: Suppose x1 and x2 are solutions; we need to show that c1x1 + c2x2 is also a...