Let Y1(x) Y2(x) be two linearly independent solutions of the homogeneous equation y''+p(x)y'+q(x)y=0. Select all of the correct statements for the two-point boundary value problem

y''+p(x)y'+q(x)y=g(x)

y(0)=y0,

y'(L)=yL'

When this two-point boundary value problem has no solution, the corresponding homogeneous equation also has no solution.

When the matrix A =

Y1(0) Y2(0)
Y1(L) Y2(L)
is invertible, the nonhomogeneous two point value problem has a unique solution for any choices of g(x), y0, yL'

When this two-point boundary value problem has infinite many solutions, the corresponding homogeneous equation also has infinite many solutions.

This two-point boundary value problem could have no solution when the corresponding homogeneous equation has non trivial solutions.

The corresponding homogeneous equation is obtained by setting g(x)=0, y0=0, yL'=0