show that if.
`y = sin 3x : then(d^(2)y)/(dx^(2)) + 9y = 0`
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"If "y=sin^(-1)x, "find "(d^(2)y)/(dx^(2)) .

If y= 5 cos x-3 sin x , prove that (d^(2)y)/(dx^(2))+y=0 .

Show that the solution y = a sin x + b cos x + x sin x satisfies , (d^(2)y)/(dx^(2)) + y = 2 cos x

If y= A sin x+ B cos x , then prove that (d^(2)y)/(dx^(2))+y=0 .

If y =sin (sin x) and (d^(2)y)/(dx^(2))+(dy)/(dx) tan x + f(x) = 0 , then find f(x) .

If y=2sin2x+3cos2x , find (d^2y)/dx^2 .

Find (d^2y)/(dx^2) , When : y=sin^3x

IF y^3=x^2+y^2 , find (d^2y)/(dx^2) at y=1.

Show that the function y= A cos 2x - B sin 2x is a solution of the differential equation (d^(2)y)/(dx^(2)) + 4y = 0

For each of the differential equations given below, indicate its order and degree(if defined). (i) (d^(2)y)/(dx^(2))+ 5x((dy)/(dx))^(2) - 6y = log x (ii) ((dy)/(dx))^(3) - 4((dy)/(dx))^(2) + 7y = sin x (iii) (d^(4)y)/(dx^(4)) - sin ((d^(3)y)/(dx^(3)) = 0