Sturm Liouville Form. All the eigenvalue are real We apply the boundary conditions a1y(a) + a2y ′ (a) = 0, b1y(b) + b2y ′ (b) = 0,
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However, we will not prove them all here. Web 3 answers sorted by: There are a number of things covered including: Share cite follow answered may 17, 2019 at 23:12 wang 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); The most important boundary conditions of this form are y ( a) = y ( b) and y ′ ( a) = y. The boundary conditions require that Web the general solution of this ode is p v(x) =ccos( x) +dsin( x): We can then multiply both sides of the equation with p, and find.
Share cite follow answered may 17, 2019 at 23:12 wang Put the following equation into the form \eqref {eq:6}: We apply the boundary conditions a1y(a) + a2y ′ (a) = 0, b1y(b) + b2y ′ (b) = 0, Web it is customary to distinguish between regular and singular problems. We can then multiply both sides of the equation with p, and find. All the eigenvalue are real We just multiply by e − x : Web so let us assume an equation of that form. Web the general solution of this ode is p v(x) =ccos( x) +dsin( x): If λ < 1 / 4 then r1 and r2 are real and distinct, so the general solution of the differential equation in equation 13.2.2 is y = c1er1t + c2er2t. P and r are positive on [a,b].
