Challenging +1.2 This is a separable differential equation requiring factorization of a cubic polynomial, integration of partial fractions, and algebraic manipulation to reach the final form. While it involves multiple steps and careful algebra, the techniques are standard A-level material (separation of variables, partial fractions, logarithmic integration). The cubic factorization and partial fraction decomposition add computational complexity beyond a routine question, but no novel insight is required, placing it moderately above average difficulty.
Find the general solution of the differential equation
$$(2x^3 - 3x^2 - 11x + 6)\frac{dy}{dx} = y(20x - 35).$$
Give your answer in the form \(y = f(x)\). [9]
Find the general solution of the differential equation
$$(2x^3 - 3x^2 - 11x + 6)\frac{dy}{dx} = y(20x - 35).$$
Give your answer in the form $y = f(x)$. [9]
\hfill \mbox{\textit{SPS SPS SM Pure 2021 Q8 [9]}}