# Questions tagged [homogeneous-equation]

A linear differential equation is called homogeneous if the following condition is satisfied: If $\phi(x)$ is a solution, so is $c \phi(x)$, where c is an arbitrary (non-zero) constant. (Def: http://en.m.wikipedia.org/wiki/Homogeneous_differential_equation)

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### Second order homogeneous linear differential equation with variables coefficients. [closed]

I'm facing an equation preventing me from moving forward in my studies. $$\frac{d^2 \delta}{dy} + \frac{2+3y}{2y(1+y)} \frac{d \delta}{dy} = \frac{3}{2} \frac{\delta}{y (1+y)}$$ I found both solutions ...
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### Nonhomogeneous nonlinear differential equation with delta functions

I'm trying to solve the following differential equation $$y'' + \dfrac{1}{2}(y')^2 = A \delta(x) + B \delta(x-a) + C$$ I tried two times, the first one using Laplace transforms, but I don't really ...
1 vote
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### Classification of Homogeneous functions

Is every homogeneous function of degree 1 in two variables is of the form $f(x,y)=\frac{p(x,y)}{q(x,y)}$, where $p(x,y)$ is a homogeneous polynomial of degree $n$ and $q(x,y)$ is a homogeneous ...
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### When and how do we dehomogenize a homogeneous function?

When and how do we dehomogenize a homogeneous function? To solve Prove the sign and zeroes of $Ax^2 + 2Bxy + Cy^2$ (without using the second derivative test) , "user" set $$t = \frac x y$$ ...
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### General Solution for a non-homogenous ordinary differential equation

The differential equation is $\frac{d^2y}{dt^2} - \frac{dy}{dt} -6y = e^{3t} - 3t^2$. I first found the homogeneous solution which I got as $$y(t) = c_1e^{-2t} + c_2e^{3t}$$ I am trying to figure out ...
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### Techniques for solving a difference recurrence relations

I’m having issues understanding how an answer is derived in a math textbook I have. Just looking for a technique for the derivation as well as some intuition to help with my understanding. The ...
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### Finding a particular solution to undetermined coefficients problem that will be part of the fundamental set

The problem at hand My working so far: I am not sure where to go from here.
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1 vote
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### How to find the summation of the following series? .

If $$S=\sum_{i=1}^{n} \frac{1}{i2^{i}},$$ Then how can I find the summation of the above series up to $n^{th}$ terms? I can't solve this question because I don't know whether this summation is a ...
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### Degree in homogeneous function in differential equations

How do we say $n$ to be degree of an equation, We have $F(kx,ky)=k^{n} F(x,y)$ then we say n is the degree of the equation but we generally consider the degree to be the highest power of a variable in ...
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### Homogeneous or Nonhomogeneous ODEs?

May I ask whether the ODEs below are 'Homogeneous' or 'Nonhomogeneous'? 1.) y'' - y' = y 2.) y'' - y' = sin(y) 3.) y'' - y' = xy Thank you for your answers!
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### Condition for lines joining origin to the point of intersection(s) of two curves to be perpendicular

Given curves: $$ax^2+2hxy+by^2+2gx=0$$ $$a_1x^2+2h_1xy+b_1y^2+2g_1x=0$$ It is given that the lines joining the origin to the points of intersection of these curves are perpendicular to each other. We'...
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### How to find a solution to a homogeneous ordinary differential equation with non-constant coefficients (the coefficients are linear functions)?

I am trying to find a solution to a differential equation in the form $$y'' + (ax+b)y' + (cx+d)y = 0,$$ where $a,b,c,d$ are constants. I only know how to solve when the coefficients are constants, and ...
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### Linear second order homogeneous matrix ODEs with constant coefficients: Solution strategies?

$\newcommand{\bm}[1]{\boldsymbol{#1}}$ $\newcommand{\img}{\operatorname{img}}$ The Scalar Setting When looking for a solution $u:\mathbb{R}\to\mathbb{R}$ of the following linear homogeneous second ...
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### When does a homogeneous equation represent a set of straight lines?

Recently I came across this question, where the top voted answer claimed that all homogeneous equation represent a set of straiight lines passing through origin. I was wondering if this was true ...
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### Solving a Lamé differential equation with a parameter out of boundaries.

I am trying to get rid of the following homogeneous ode. \begin{split} u''(z)+\frac{1}{2} \left(\frac{1}{z}+\frac{1}{z-1}+\frac{1}{z-1}\right) u'(z)+\frac{2\left(A+B\right)- \left(2 ...
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