First-order differential equations and integrating factors

First-order differential equations and integrating factors Quiz

Spec 9.1–2 · Edexcel A-Level Further Maths: Quiz

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  1. 1. What is the integrating factor for xdydx+3y=x2x\frac{dy}{dx}+3y=x^2 with x>0x>0?

    • A. xx
    • B. x3x^3
    • C. e3xe^{3x}
    • D. 3ln⁡x3\ln x

  2. 2. What is the integrating factor for dydx+4y=ex\frac{dy}{dx}+4y=e^{x}?

    • A. e4xe^{4x}
    • B. exe^{x}
    • C. 4x4x
    • D. e−4xe^{-4x}

  3. 3. Find the general solution of dydx+2y=6\frac{dy}{dx}+2y=6.

    • A. y=3+ce2xy=3+ce^{2x}
    • B. y=6+ce−2xy=6+ce^{-2x}
    • C. y=3+ce−2xy=3+ce^{-2x}
    • D. y=3e−2x+cy=3e^{-2x}+c

  4. 4. All solution curves of dydx+y=2\frac{dy}{dx}+y=2 approach which line as x→∞x\to\infty?

    • A. y=0y=0
    • B. y=cy=c
    • C. x=2x=2
    • D. y=2y=2

  5. 5. A tank satisfies dmdt=3−m20\frac{dm}{dt}=3-\frac{m}{20}. What mass does mm approach in the long term?

    • A. 3
    • B. 20
    • C. 60
    • D. 23

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