Sturm Liouville Form. Web it is customary to distinguish between regular and singular problems. Put the following equation into the form \eqref {eq:6}:
5. Recall that the SturmLiouville problem has
However, we will not prove them all here. We apply the boundary conditions a1y(a) + a2y ′ (a) = 0, b1y(b) + b2y ′ (b) = 0, Α y ( a) + β y ’ ( a ) + γ y ( b ) + δ y ’ ( b) = 0 i = 1, 2. For the example above, x2y′′ +xy′ +2y = 0. We just multiply by e − x : The solutions (with appropriate boundary conditions) of are called eigenvalues and the corresponding eigenfunctions. Share cite follow answered may 17, 2019 at 23:12 wang P, p′, q and r are continuous on [a,b]; Web the general solution of this ode is p v(x) =ccos( x) +dsin( x): (c 1,c 2) 6= (0 ,0) and (d 1,d 2) 6= (0 ,0);
Web 3 answers sorted by: Put the following equation into the form \eqref {eq:6}: Web it is customary to distinguish between regular and singular problems. We can then multiply both sides of the equation with p, and find. If the interval $ ( a, b) $ is infinite or if $ q ( x) $ is not summable. Web so let us assume an equation of that form. However, we will not prove them all here. All the eigenvalue are real Web the general solution of this ode is p v(x) =ccos( x) +dsin( x): We apply the boundary conditions a1y(a) + a2y ′ (a) = 0, b1y(b) + b2y ′ (b) = 0, The solutions (with appropriate boundary conditions) of are called eigenvalues and the corresponding eigenfunctions.
