Coupled first-order differential equations

Coupled first-order differential equations Quiz

Spec 9.9 · Edexcel A-Level Further Maths: Quiz

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  1. 1. For x˙=x+y\dot{x}=x+y, y˙=4x+y\dot{y}=4x+y, eliminating yy gives which equation?

    • A. x¨−2x˙−3x=0\ddot{x}-2\dot{x}-3x=0
    • B. x¨+2x˙−3x=0\ddot{x}+2\dot{x}-3x=0
    • C. x¨−2x˙+3x=0\ddot{x}-2\dot{x}+3x=0
    • D. x¨−2x˙−5x=0\ddot{x}-2\dot{x}-5x=0

  2. 2. For the same system, what is the general solution for xx?

    • A. Ae−3t+BetAe^{-3t}+Be^{t}
    • B. (A+Bt)e3t(A+Bt)e^{3t}
    • C. Ae3t+Be−tAe^{3t}+Be^{-t}
    • D. Ae2t+Be−2tAe^{2t}+Be^{-2t}

  3. 3. Using y=x˙−xy=\dot{x}-x with x=Ae3t+Be−tx=Ae^{3t}+Be^{-t}, find yy.

    • A. Ae3t+Be−tAe^{3t}+Be^{-t}
    • B. 3Ae3t−Be−t3Ae^{3t}-Be^{-t}
    • C. 2Ae3t+2Be−t2Ae^{3t}+2Be^{-t}
    • D. 2Ae3t−2Be−t2Ae^{3t}-2Be^{-t}

  4. 4. For x˙=−2x+y\dot{x}=-2x+y, y˙=x−2y+9\dot{y}=x-2y+9, what is the equilibrium point (x,y)(x,y)?

    • A. (9,9)(9,9)
    • B. (3,6)(3,6)
    • C. (6,3)(6,3)
    • D. (0,0)(0,0)

  5. 5. Why should you find the second variable from an original equation rather than solving separately?

    • A. Both are equally valid
    • B. The second equation has no solution
    • C. It avoids extra constants that need not satisfy both equations
    • D. It makes yy equal to xx

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