Second order equations with constant coefficients

Second order equations with constant coefficients Quiz

Spec I4 · AQA A-Level Further Maths: Quiz

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  1. 1. Find the general solution of y′′−3y′+2y=0y''-3y'+2y=0.

    • A. y=Ae−x+Be−2xy=Ae^{-x}+Be^{-2x}
    • B. y=(A+Bx)exy=(A+Bx)e^{x}
    • C. y=Aex+Be2xy=Ae^{x}+Be^{2x}
    • D. y=Ae3x+Be2xy=Ae^{3x}+Be^{2x}

  2. 2. Find the general solution of y′′+9y=0y''+9y=0.

    • A. y=Acos⁡3x+Bsin⁡3xy=A\cos3x+B\sin3x
    • B. y=Ae3x+Be−3xy=Ae^{3x}+Be^{-3x}
    • C. y=(A+Bx)e3xy=(A+Bx)e^{3x}
    • D. y=e3x(Acos⁡x+Bsin⁡x)y=e^{3x}(A\cos x+B\sin x)

  3. 3. Find the general solution of y′′−6y′+9y=0y''-6y'+9y=0.

    • A. y=Ae3x+Be−3xy=Ae^{3x}+Be^{-3x}
    • B. y=(A+Bx)e−3xy=(A+Bx)e^{-3x}
    • C. y=Ae3x+Be3xy=Ae^{3x}+Be^{3x}
    • D. y=(A+Bx)e3xy=(A+Bx)e^{3x}

  4. 4. The auxiliary equation has roots −2±3i-2\pm3i. The general solution is

    • A. y=e3x(Acos⁡2x+Bsin⁡2x)y=e^{3x}(A\cos2x+B\sin2x)
    • B. y=e−2x(Acos⁡3x+Bsin⁡3x)y=e^{-2x}(A\cos3x+B\sin3x)
    • C. y=Ae−2x+Be3xy=Ae^{-2x}+Be^{3x}
    • D. y=(A+Bx)e−2xy=(A+Bx)e^{-2x}

  5. 5. To find both constants in the general solution of a second-order equation you need

    • A. one condition on yy
    • B. the value of y′′y'' only
    • C. two independent conditions
    • D. three conditions

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