Second-order linear differential equations

Second-order linear differential equations Quiz

Spec 9.4–6 · Edexcel A-Level Further Maths: Quiz

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  1. 1. Find the roots of the auxiliary equation for y′′−7y′+12y=0y''-7y'+12y=0.

    • A. m=−3, m=−4m=-3,\ m=-4
    • B. m=3, m=4m=3,\ m=4
    • C. m=7, m=12m=7,\ m=12
    • D. m=−7, m=−12m=-7,\ m=-12

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

  3. 3. Find the general solution of y′′+16y=0y''+16y=0.

    • A. y=Acos⁡4x+Bsin⁡4xy=A\cos4x+B\sin4x
    • B. y=Ae4x+Be−4xy=Ae^{4x}+Be^{-4x}
    • C. y=Acos⁡16x+Bsin⁡16xy=A\cos16x+B\sin16x
    • D. y=e4x(Acos⁡x+Bsin⁡x)y=e^{4x}(A\cos x+B\sin x)

  4. 4. For y′′+3y′+2y=5e−xy''+3y'+2y=5e^{-x}, which trial particular integral should you use?

    • A. ke−xke^{-x}
    • B. kxexkxe^{x}
    • C. kxe−xkxe^{-x}
    • D. kx2e−xkx^2e^{-x}

  5. 5. Which trial particular integral suits y′′+y′+y=3x2+1y''+y'+y=3x^2+1?

    • A. ax2+bax^2+b
    • B. ax2+bx+cax^2+bx+c
    • C. aexae^{x}
    • D. acos⁡x+bsin⁡xa\cos x+b\sin x

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