Express 4x+5(x+2)(2x+1)\displaystyle \frac{4x + 5}{(x + 2)(2x + 1)}(x+2)(2x+1)4x+5 in partial fractions
Given that x>0x > 0x>0, find the general solution to the differential equation
(x+2)(2x+1)dydx=y(4x+5) (x + 2)(2x + 1) \frac{dy}{dx} = y(4x + 5) (x+2)(2x+1)dxdy=y(4x+5)Hence find the particular solution to the differential equation that satisfies y=24y = 24y=24 at x=1x = 1x=1, 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.
