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searching for Homogeneous differential equation 14 found (25 total)

alternate case: homogeneous differential equation

Unified framework (1,548 words) [view diff] exact match in snippet view article find links to article

perturbation of modes and natural frequencies, the initial homogeneous differential equation with nonconstant coefficients is changed to a series of non-homogeneous

Kneser's theorem (differential equations) (859 words) [view diff] exact match in snippet view article

with continuous right hand side. Consider an ordinary linear homogeneous differential equation of the form y ″ + q ( x ) y = 0 {\displaystyle y''+q(x)y=0}

Relaxation (physics) (1,537 words) [view diff] exact match in snippet view article

an exponential law exp(−t/τ) (exponential decay). Let the homogeneous differential equation: m d 2 y d t 2 + γ d y d t + k y = 0 {\displaystyle m{\frac

George Pólya (1,801 words) [view diff] exact match in snippet view article find links to article

"On the mean-value theorem corresponding to a given linear homogeneous differential equation". Trans. Amer. Math. Soc. 24 (4): 312–324. doi:10

Reduction of order (1,610 words) [view diff] exact match in snippet view article find links to article

) {\displaystyle y_{1}(t)} is a solution of the original homogeneous differential equation, y 1 ″ ( t ) + p ( t ) y 1 ′ ( t ) + q ( t ) y 1 ( t ) = 0

Bessel–Clifford function (1,213 words) [view diff] exact match in snippet view article find links to article

{\mathcal {C}}_{n}(x)} satisfies the linear second-order homogeneous differential equation x y ″ + ( n + 1 ) y ′ = y . {\displaystyle xy''+(n+1)y'=y

Fixed-point iteration (2,172 words) [view diff] exact match in snippet view article find links to article

Lyapunov stable but not attracting. The center of a linear homogeneous differential equation of the second order is an example of a neutrally stable fixed

Jacobi polynomials (2,449 words) [view diff] exact match in snippet view article find links to article

P_{n}^{(\alpha ,\beta )}} is a solution of the second order linear homogeneous differential equation: IV.2 ( 1 − x 2 ) y ″ + ( β − α − ( α + β + 2 ) x ) y ′ +

Laplace's equation (5,075 words) [view diff] exact match in snippet view article find links to article

functions are solutions to Laplace's equation (or any linear homogeneous differential equation), their sum (or any linear combination) is also a solution

Complex affine space (2,538 words) [view diff] exact match in snippet view article find links to article

linear ordinary differential equations. The solutions of the homogeneous differential equation y ′ ( x ) + μ ( x ) y ( x ) = 0 {\displaystyle y'(x)+\mu (x)y(x)=0}

Projectile motion (5,766 words) [view diff] exact match in snippet view article find links to article

{d} t}}+\mu v_{y}=-g} (2a) This first order, linear, non-homogeneous differential equation may be solved a number of ways; however, in this instance

Fourier transform (21,314 words) [view diff] exact match in snippet view article find links to article

{C} .} A set of eigenfunctions is found by noting that the homogeneous differential equation [ U ( 1 2 π d d x ) + U ( x ) ] ψ ( x ) = 0 {\displaystyle

Matrix exponential (10,481 words) [view diff] exact match in snippet view article find links to article

differential equation.) Recall from earlier in this article that a homogeneous differential equation of the form y ′ = A y {\displaystyle \mathbf {y} '=A\mathbf

Geodesics on an ellipsoid (8,506 words) [view diff] exact match in snippet view article find links to article

is the Gaussian curvature at s. As a second order, linear, homogeneous differential equation, its solution may be expressed as the sum of two independent