Express 3x−3(x+1)(2x−1)\displaystyle \frac{3x - 3}{(x + 1)(2x - 1)}(x+1)(2x−1)3x−3 in partial fractions
Given that x>1x > 1x>1, find the general solution to the differential equation
(x+1)(2x−1)dydx=y(3x−3) (x + 1)(2x - 1) \frac{dy}{dx} = y(3x - 3) (x+1)(2x−1)dxdy=y(3x−3)Hence find the particular solution to the differential equation that satisfies y=6y = 6y=6 at x=5x = 5x=5, giving your answer in the form y=f(x)y = f(x)y=f(x)
Practise AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
