Higher Derivatives Question

Hi all,

Here goes the question:

Given that $\displaystyle y=xsin3x+cos3x$, show that $\displaystyle x^2\frac{d^2y}{dx^2}+2y+4x^2y=0$.

I am quite comfortable in deriving the normal and higher derivatives(*Just to make sure I am on the right track, is $\displaystyle \frac{dy}{dx}$=sin3x-3sin3x+3xcos3x?) and am more concerned about the 'showing' part. Hopefully someone can guide me along.

Another one:

Given that $\displaystyle xy=sinx$, prove that $\displaystyle \frac{d^2y}{dx^2}+\frac{2}{x}\frac{dy}{dx}+y=0$.

It seems like a typical implicit diff. question other than the higher derivatives part. I haven't really learn how to derive higher derivatives using implicit diff.

Any help is appreciated. Thanks in advance!