Sturm Liouville Form. We just multiply by e − x : Share cite follow answered may 17, 2019 at 23:12 wang
Sturm Liouville Differential Equation YouTube
We can then multiply both sides of the equation with p, and find. The functions p(x), p′(x), q(x) and σ(x) are assumed to be continuous on (a, b) and p(x) >. The most important boundary conditions of this form are y ( a) = y ( b) and y ′ ( a) = y. There are a number of things covered including: P, p′, q and r are continuous on [a,b]; Where α, β, γ, and δ, are constants. If the interval $ ( a, b) $ is infinite or if $ q ( x) $ is not summable. The boundary conditions (2) and (3) are called separated boundary. Web it is customary to distinguish between regular and singular problems. Α y ( a) + β y ’ ( a ) + γ y ( b ) + δ y ’ ( b) = 0 i = 1, 2.
Put the following equation into the form \eqref {eq:6}: The boundary conditions require that Where α, β, γ, and δ, are constants. We apply the boundary conditions a1y(a) + a2y ′ (a) = 0, b1y(b) + b2y ′ (b) = 0, All the eigenvalue are real E − x x y ″ + e − x ( 1 − x) y ′ ⏟ = ( x e − x y ′) ′ + λ e − x y = 0, and then we get ( x e − x y ′) ′ + λ e − x y = 0. (c 1,c 2) 6= (0 ,0) and (d 1,d 2) 6= (0 ,0); Such equations are common in both classical physics (e.g., thermal conduction) and quantum mechanics (e.g., schrödinger equation) to describe. P and r are positive on [a,b]. Web it is customary to distinguish between regular and singular problems. Web so let us assume an equation of that form.
