Express 7x+3(x−1)(3x+2)\displaystyle \frac{7x + 3}{(x - 1)(3x + 2)}(x−1)(3x+2)7x+3 in partial fractions
Given that x>1x > 1x>1, find the general solution to the differential equation
(x−1)(3x+2)dydx=y(7x+3) (x - 1)(3x + 2) \frac{dy}{dx} = y(7x + 3) (x−1)(3x+2)dxdy=y(7x+3)Hence find the particular solution to the differential equation that satisfies y=12y = 12y=12 at x=2x = 2x=2, giving your answer in the form y=f(x)y = f(x)y=f(x)
