Homogeneous Equation definition of Homogeneous Equation in the Free Online Encyclopedia.

homogeneous equation [‚hä·mə′jē·nē·əs i′kwā·zhən]

(mathematics)

An equation that can be rewritten into the form having zero on one side of the equal sign and a homogeneous function of all the variables on the other side.

Homogeneous Equation

an equation whose form does not change upon simultaneous multiplication of all or only some unknowns by a given arbitrary number. In the latter case, the equation is said to be homogeneous with respect to the corresponding unknowns. For example, xy + yz + zx = 0 is a homogeneous equation with respect to all unknowns, and the equation y + ln (x/z) + 5 = 0 is homogeneous with respect to x and z. The left-hand member of a homogeneous equation is a homogeneous function. The equation

a₀(x)y⁽ⁿ⁾ + a₁(x)y^(n-1) + … + a_n(x)y = 0

which is called a linear homogeneous differential equation, is homogeneous with respect to y, y′, …,y^(n-1), y(n). The equation y′ = f(x, y), where f(x, y) = f (λx, λy) for any λ [f(x, y) is a homogeneous function with a degree of homogeneity 0], is said to be a differentia) equation homogeneous with respect to the variables x and y. For example, y′ = xy/(x² + y²).

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No references found			3) be the solution of the homogeneous equation [[dv]/[dx]] = Av (4. Eigenvalue approach to three dimensional coupled thermoelasticity in ... by Das, N.C.; Lahiri, A.; Sarkar, S. / Tamsui Oxford Journal of Mathematical Sciences Furthermore, it allows an easy-comparison of the general solution of a first-order linear differential homogeneous equation 2. A course on ordinary differential equations by De La Sen, M. / Academic Exchange Quarterly u]) = 0 for all u, (A4) is a system of homogeneous equations whose matrix of coefficients has a rank of (n - 1). Dynamic implications of capital market perfection by Sinha, Deepak K. / Southern Economic Journal			homodynamic Homodynamy homodyne receiver homodyne reception Homoeans homoecious homoeomerous Homoeomery Homoeosis homoerotism homofermentative lactobacilli Homoforms homogametic sex Homogamety homogamous Homogamy Homogenate homogeneity homogeneous homogeneous atmosphere homogeneous catalysis homogeneous chemical reaction Homogeneous Coordinates homogeneous differential equation homogeneous environment Homogeneous Equation Homogeneous Function homogeneous integral equation homogeneous line-broadening homogeneous material homogeneous network homogeneous nucleation homogeneous polynomial homogeneous radiation Homogeneous Reactor homogeneous space homogeneous strain Homogeneous System homogeneous transformation homogeneously staining region Homogenization homogenize Homogenizer homogenous homogentisase Homogentisic Acid homogony homograft homograft rejection homographic transformations homoiochlamydeous			homogeneity homogeneity Homogeneity (psychometrics) Homogeneity (psychometrics) Homogeneity (psychometrics) Homogeneity (psychometrics) Homogeneity (psychometrics) Homogeneity of variance Homogeneity, Miscibility & Foam Test homogeneous homogeneous homogeneous homogeneous homogeneous Homogeneous Assembly Zero Energy Laboratory homogeneous atmosphere Homogeneous Bent Function Homogeneous Bright QSO Homogeneous catalysis Homogeneous catalyst Homogeneous Charge Progressive Combustion Homogeneous Charge-Compression Ignition homogeneous chemical reaction Homogeneous co-ordinates Homogeneous coordinate Homogeneous coordinates Homogeneous differential equation Homogeneous Electron Gas Homogeneous Enhancing Lesion homogeneous environment Homogeneous Equation Homogeneous expectations assumption Homogeneous Expectations Assumptions Homogeneous form Homogeneous form Homogeneous function homogeneous integral equation Homogeneous Isotropic Dielectric homogeneous line-broadening Homogeneous linear transformation homogeneous material Homogeneous matter Homogeneous matter Homogeneous matter Homogeneous matter Homogeneous mixture Homogeneous mixture Homogeneous mixture Homogeneous mixture homogeneous network homogeneous nucleation Homogeneous Poisson Clustered Model Homogeneous Poisson Process Homogeneous polynomial Homogeneous polynomial Homogeneous Polynomial Lyapunov Function homogeneous polynomial vector field Homogeneous products Homogeneous products Homogeneous products Homogeneous products