PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Ordinary differential equations · Ordinary differential equations
Conditions of Validity, Ch Linear ordinary differential equations: existence, the Wronskian, and a kernel in disguise
Problem
Consider the purely mathematical, dimensionless linear equation y′′+9y=f(x), with homogeneous solutions y1(x)=cos3x and y2(x)=sin3x.
((a)) Construct the initial-value Green function G(x,ξ) for this operator.
((b)) Verify that G is continuous at x=ξ and that ∂G/∂x jumps by the amount the jump condition predicts.
((c)) Evaluate G(x,ξ) when x−ξ=π/6.