Series solutions and reducible differential equations

Series solutions and reducible differential equations Quiz

Spec 3.1–2 · Edexcel A-Level Further Maths: Quiz

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  1. 1. For y′′+xy′+y=0y''+xy'+y=0, y(0)=1y(0)=1, y′(0)=0y'(0)=0, what is y′′(0)y''(0)?

    • A. 11
    • B. 00
    • C. −1-1
    • D. 22

  2. 2. If y′=x−y2y'=x-y^2, then y′′=y''=

    • A. 1−2y1-2y
    • B. 1−2yy′1-2yy'
    • C. −2yy′-2yy'
    • D. 1+2yy′1+2yy'

  3. 3. With z=1yz=\frac1y, dydx\frac{\mathrm{d}y}{\mathrm{d}x} equals

    • A. 1z2dzdx\frac{1}{z^2}\frac{\mathrm{d}z}{\mathrm{d}x}
    • B. −1zdzdx-\frac{1}{z}\frac{\mathrm{d}z}{\mathrm{d}x}
    • C. −z2dzdx-z^2\frac{\mathrm{d}z}{\mathrm{d}x}
    • D. −1z2dzdx-\frac{1}{z^2}\frac{\mathrm{d}z}{\mathrm{d}x}

  4. 4. With x=etx=\mathrm{e}^t, d2ydx2\frac{\mathrm{d}^2y}{\mathrm{d}x^2} equals

    • A. 1x2d2ydt2\frac{1}{x^2}\frac{\mathrm{d}^2y}{\mathrm{d}t^2}
    • B. 1x2(d2ydt2−dydt)\frac{1}{x^2}\left(\frac{\mathrm{d}^2y}{\mathrm{d}t^2}-\frac{\mathrm{d}y}{\mathrm{d}t}\right)
    • C. 1xd2ydt2\frac{1}{x}\frac{\mathrm{d}^2y}{\mathrm{d}t^2}
    • D. 1x2(d2ydt2+dydt)\frac{1}{x^2}\left(\frac{\mathrm{d}^2y}{\mathrm{d}t^2}+\frac{\mathrm{d}y}{\mathrm{d}t}\right)

  5. 5. The equation d2ydt2−3dydt+2y=0\frac{\mathrm{d}^2y}{\mathrm{d}t^2}-3\frac{\mathrm{d}y}{\mathrm{d}t}+2y=0 has complementary function

    • A. Aet+Be2tA\mathrm{e}^{t}+B\mathrm{e}^{2t}
    • B. Ae−t+Be−2tA\mathrm{e}^{-t}+B\mathrm{e}^{-2t}
    • C. Aet+Be3tA\mathrm{e}^{t}+B\mathrm{e}^{3t}
    • D. (A+Bt)et(A+Bt)\mathrm{e}^{t}

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