P, p′, q and r are continuous on [a,b]; Web solution the characteristic equation of equation 13.2.2 is r2 + 3r + 2 + λ = 0, with zeros r1 = − 3 + √1 − 4λ 2 and r2 = − 3 − √1 − 4λ 2. We will merely list some of the important facts and focus on a few of the properties. There are a number of things covered including: The solutions (with appropriate boundary conditions) of are called eigenvalues and the corresponding eigenfunctions. The most important boundary conditions of this form are y ( a) = y ( b) and y ′ ( a) = y. However, we will not prove them all here. Where is a constant and is a known function called either the density or weighting function. Web it is customary to distinguish between regular and singular problems. Where α, β, γ, and δ, are constants.
Web the general solution of this ode is p v(x) =ccos( x) +dsin( x): The most important boundary conditions of this form are y ( a) = y ( b) and y ′ ( a) = y. We will merely list some of the important facts and focus on a few of the properties. Web the general solution of this ode is p v(x) =ccos( x) +dsin( x): Basic asymptotics, properties of the spectrum, interlacing of zeros, transformation arguments. Put the following equation into the form \eqref {eq:6}: We just multiply by e − x : (c 1,c 2) 6= (0 ,0) and (d 1,d 2) 6= (0 ,0); Α y ( a) + β y ’ ( a ) + γ y ( b ) + δ y ’ ( b) = 0 i = 1, 2. P, p′, q and r are continuous on [a,b]; Where α, β, γ, and δ, are constants.
