Green's function for y''+4y=f(x) with y(0)=0, y'(1)=0

[sassie]

Consider the BVP

y''+4y=f(x) (0$$\leq$$x$$\leq$$1)
y(0)=0 y'(1)=0

Find the Green's function (two-sided) for this problem.

Working: So firstly, I let y(x)=Asin2x+Bcos2x

Then using the boundary conditions,

Asin(2.0)+Bcos(2.0)=0 => B=0

y'(x)=2Acos(2x)-2Asin(2x)
y'(0)=2A=0 => A=0

But is this right? How can I derive a Green's function (two-sided) from this? Please help.

 

[sassie]

Please ignore. I figured out what I did wrong.