1. A

    Solving Homogeneous Equation

    Hi, I have attached part of my steps for solving the homogeneous equation. The equation is proven to be homogeneous. However after using substitution of y=zx and its' derivative, I was not able to separate the variables conveniently as shown. Please advise. Thank you!
  2. ProofOfALifetime

    Homogeneous Functions

    I've been working on a few inequality proofs over the last few months, and some of the solutions I've looked at mentioned that since the inequality is homogeneous, you can make extra condtions like $abc=1$ or $a+b+c=1$ or others. What I don't get is how can you tell if an inequality is...
  3. I

    Homogeneous solution explain

    Given equation y'+py=q for q=0 then y=y_h is the homogeneous solution (1) Explain why solution to equation is y=y_h+y_p where y_h - homogeneous and y_p -particular (2) Explain how to derive y_p from y_h How to derive y=y_h + y_p ?
  4. I

    Homogeneous function

    Hello :) Can you explain me please about the next exercise (solution): Given to us: degree of homogeneity is 0.5, x=y, elevation of X1 is double from elevation of X0 (if elevation of X0 is c, so elevation of X1 is 2*c). What is degree of homogeneity...
  5. C

    Example of questions of Non Homogeneous first-order linear differential equations?

    Hi people! I tried to look around the internet for questions that use the method in the pic to solve the differential equations. But I can't seem to find any. Do you have any examples for me? I am not familiar with ODE, but I was asked to help someone else. Thanks! =)
  6. B

    Difference between 2 homogeneous matrices.

    Hey, I'm currently working on a project and would like to ask a question: Given a homogeneous matrix with coordinates of an object. The objects moves, lets say +10 along the x axis and a rotates along the y axis. Now we have 2 matrices, the old one and the new one. The question is, what is...
  7. Z

    rref rank nullity and homogeneous linear equations

    rref (reduced row echelon form) of the matrix of a homogeneous system can be illustrated with column labels as: \begin{matrix} x_1 &x_2 &x_3 &x_4 &x_5 \\ 1 &0 &a_1 &a_2 &a_3 \\ 0& 1 &b_1 &b_2 &b_3 \end{matrix} Note row rank = column rank. The solution (null) space is spanned by...
  8. R

    Discrete Mathematics: Linear homogeneous recurrence of order 2

    Well i've learned the solution of solving linear homogeneous recurrence equations of the second order from the book "discrete and combinatorial mathematics" of Ralph Grimaldi. But there was just an unclear tutorial of the solution with no explanation on how this solution is made, what's its...
  9. BonaviaFx

    Homogeneous Equation Problem

    Any help or hints are appreciated. Find the general solution of the following, using the substitution y=vx. Problem: \frac{dy}{dx} = \frac{y+√(x²-y²)}{x} I worked out a couple of these so I'm pretty familiar on the working.
  10. F

    Homogeneous Equations

    Hello everyone, I do this problem from Homogeneous Equations ...... but I don't know how I can complete the problem .... please help me and how I know my answer is true? thanks
  11. J

    Particular Solution for homogeneous case

    Hi math experts: given ODE: y''+3y'+2y = 0 (actually I expect that it should be "-3y") g(x)=exp(5x) Particular solution: y=c*exp(5x) (given as solution) But... I do not get that solution... I am stuck, can anybody help? Thanks!
  12. H

    Initial value & mass-spring equation problems- please help!

    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...
  13. J

    Non-trivial solution of a homogeneous system

    Hello, I'm stuck with this question. Can anyone help me? :) Find all values of k for which this homogeneous system has non-trivial solutions: [kx + 5y + 3z = 0 [5x + y - z = 0 [kx + 2y + z = 0 I made the matrix, but I don't really know which Gauss-elimination method I should use to get the...
  14. H

    Homogeneous function-a doubt

    Can a function f(x,y) be a homogeneous function of degree n where n is a decimal number? I have a problem which asks me to find the degree of homogeneity of a given function. I find the degree of homogeneity to be 1.5. Now I am confused because I don't know if the degree can be a decimal number...
  15. C

    A question about homogeneous of degree

    If f is homogeneous of degree n, show that fx(tx,ty)=t^(n-1)fx(x,y) fx: regard y as a constant and differentiate f(x,y)with respect to x. Proof: ?f is homogeneous, ?f(tx,ty)=t^n*f(x,y) ? differentiate both sides with respect to x, Then [df/d(tx)]*[d(tx)/ d(x)]+ [df/d(ty)]*[d(ty)/dx]=t^n*fx(x,y)...
  16. R


    Hi all could please check my answer number 1 and 3 thanks
  17. R

    Non- homogeneous

    Hi could please help me in question number 1 and 3
  18. E

    Using Euler's theorem of homogeneous functions

    Been stuck on this question: show g is homogeneous of degree k and state the value of k. g(x, y)=\frac {x^3 +3xy^2}{ \sqrt[3]{x^2-y^2}} So i've been trying to use: kg(x,y)=x\dfrac{\delta g}{\delta x}+y\dfrac{\delta g}{\delta y} but i just can't seem to get a solution for k. Am i going...
  19. L

    Homogeneous Eqn of Line given 2 homogeneous points

    I'm reviewing Projective Geometry. This is an exercise in 2D homogeneous points and lines. Given two points p1 (X1,Y1,W1) and p2 (X2,Y2,W2), find u = (a, b, c) of the line (aX + bY + cW = 0). (See http://vision.stanford.edu/~birch/projective/node4.html, "Similarly, given two points p1 and p2...