d^2y/dx^2 = 18sinx................... let dy/dx = p
⇒d^2y/dx^2 = dp/dx
...dp/dx = 18sin3x....... dp = 18sin3x.dx
⇒p = -54cos3x + c............... but when x = pi/6 , y = -2
.: c = 27sqrt(2)
again, from...........p = -54cos3x + c
⇒dy/dx = -54cos3x + 27sqrt(2)................⇒dy = {-54cos3x + 27sqrt(2)}dx
.: y = -162sin3x + 27xsqrt(2) + A
Again... when x = pi/6 , y = -2
⇒A = sqrt(2){81 - 27.pi/6} - 2
.: y = -162sin3x + 27sqrt(2) + sqrt(2){81 - 27.pi/6} - 2..............[required equation]