# homogeneous

1. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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+âˆš(xÂ²-yÂ²)}{x} I worked out a couple of these so I'm pretty familiar on the working.

gebra
11. ### 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
12. ### 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!

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...
14. ### 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...
15. ### 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...
16. ### 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)...
17. ### homogeneous

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