Particular integrals

Particular integrals Quiz

Spec I5 · AQA A-Level Further Maths: Quiz

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5 questions, one answer each

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  1. 1. Choose the trial function for a PI of y′′+2y′+5y=3x2y''+2y'+5y=3x^2.

    • A. y=px2y=px^2
    • B. y=pcos⁡x+qsin⁡xy=p\cos x+q\sin x
    • C. y=px2+qx+ry=px^2+qx+r
    • D. y=pe3xy=pe^{3x}

  2. 2. Choose the trial function for a PI of y′′+4y′+3y=5sin⁡2xy''+4y'+3y=5\sin2x.

    • A. y=pcos⁡2x+qsin⁡2xy=p\cos2x+q\sin2x
    • B. y=psin⁡2xy=p\sin2x
    • C. y=pe2xy=pe^{2x}
    • D. y=psin⁡x+qcos⁡xy=p\sin x+q\cos x

  3. 3. For y′′−5y′+6y=e2xy''-5y'+6y=e^{2x}, the trial function for a PI is

    • A. y=pe2xy=pe^{2x}
    • B. y=pe−2xy=pe^{-2x}
    • C. y=p+qxy=p+qx
    • D. y=pxe2xy=pxe^{2x}

  4. 4. Find a particular integral of y′′+4y=8y''+4y=8.

    • A. y=1y=1
    • B. y=2y=2
    • C. y=4y=4
    • D. y=8y=8

  5. 5. In y=CF+PIy=\text{CF}+\text{PI}, the CF is the general solution of

    • A. y′′+ay′+by=f(x)y''+ay'+by=f(x)
    • B. y′+ay=f(x)y'+ay=f(x)
    • C. y′′+ay′+by=0y''+ay'+by=0
    • D. y′′=f(x)y''=f(x)

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