Solve for i(t) for t>0 in the circuit of the above figure with R=50 ohms given t

Question

Solve for i(t) for t>0 in the circuit of the above figure with R=50 ohms given that i(0+)=0 and vc(0+)=20 V. [Hint: Try a particular solution of the form ip(t)=Acos(100t)+Bsin(100t)

I've attempted a solution for this problem but I'm really uncomfortable with it. 

Started with:

Then eventually to:

added them to I and set them equal to 2000cos(100t)

Then I cancelled values to get

-Asin100t+Bcos100t=2000cos100t

So does A=0 and B=2000?

then ip(t)=2000sin100t???

I don't feel like I have all of the pieces together correctly here. Also do I have to do anything with alpha=R/2L or omega=1/sqrt(LC)??? 

HELP! THis is an SOS situation!

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