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Particular integralsAQA A-Level Further Maths: Flashcards

What these 13 flashcards ask

  • State the form of the general solution of y''+ay'+by=f(x).
  • What is the complementary function?
  • What is a particular integral?
  • Trial PI for f(x)=12x?
  • Trial PI for f(x)=3x^2?
  • Trial PI for f(x)=ke^{\lambda x}?
  • Trial PI for f(x)=\cos\omega x?
  • Why include both \cos and \sin in the trial?
  • What do you do after substituting the trial function?
  • What if f(x) is already in the CF?
  • Trial PI for y''-3y'+2y=4e^{x}?
  • When do you apply initial conditions?
  • What happens to the CF terms for large x if all roots have negative real part?

Exam questions on Particular integrals

  1. d2ydx2−dydx−6y=12x\frac{d^2y}{dx^2}-\frac{dy}{dx}-6y=12x.
    Find a particular integral.2 marks
  2. d2ydx2−4dydx+3y=16e−x\frac{d^2y}{dx^2}-4\frac{dy}{dx}+3y=16e^{-x}.
    Find the general solution.2 marks
  3. d2ydx2+3dydx+2y=10cos⁡x\frac{d^2y}{dx^2}+3\frac{dy}{dx}+2y=10\cos x.
    Find a particular integral.3 marks
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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).