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**sigma1** given that $\displaystyle x^2 y=3cos 2x$ show that $\displaystyle x^2 d^2y/dx^2 + 4x dy/dx +(4^2+2)y= 0$

i have

$\displaystyle x^2y + x^2 dy/dx = -2x(3sinx) + 3cos 2x $ did i differenciate the RHS correctly.. that is $\displaystyle 3cos 2x$

differentiating it again i have $\displaystyle x^2y + x^2 dy/dx+x^2 d^2y/dx^2 = -2x(3sinx) + x^2 y$

now rewriting $\displaystyle x^2 d^2y/dx^2+2x^2 dy/dx+2x(3sinx)=0$

i cant get that to look like $\displaystyle x^2 d^2y/dx^2 + 4x dy/dx +(4^2+2)y= 0$

did i do something wrong in the process.