First order equations and integrating factors

First order equations and integrating factors Quiz

Spec I1–I2 · AQA A-Level Further Maths: Quiz

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  1. 1. Find the integrating factor for dydx+2xy=x\frac{dy}{dx}+\frac2xy=x, x>0x>0.

    • A. e2xe^{2x}
    • B. x2x^2
    • C. 2ln⁡x2\ln x
    • D. x−2x^{-2}

  2. 2. Find the integrating factor for dydx−1xy=x2\frac{dy}{dx}-\frac1xy=x^2, x>0x>0.

    • A. xx
    • B. e−xe^{-x}
    • C. −ln⁡x-\ln x
    • D. 1x\frac1x

  3. 3. After multiplying dydx+P(x)y=Q(x)\frac{dy}{dx}+P(x)y=Q(x) by the integrating factor II, the left-hand side equals

    • A. ddx(Iy)\frac{d}{dx}(Iy)
    • B. ddx(y/I)\frac{d}{dx}(y/I)
    • C. IdydxI\frac{dy}{dx}
    • D. IPyIPy

  4. 4. Solve dydx+y=e−x\frac{dy}{dx}+y=e^{-x}.

    • A. y=e−x+cy=e^{-x}+c
    • B. y=(x+c)exy=(x+c)e^{x}
    • C. y=(x+c)e−xy=(x+c)e^{-x}
    • D. y=ce−xy=ce^{-x}

  5. 5. Which equation can be solved with an integrating factor?

    • A. dydx+y2=x\frac{dy}{dx}+y^2=x
    • B. dydx+xy=sin⁡x\frac{dy}{dx}+xy=\sin x
    • C. ydydx+x=1y\frac{dy}{dx}+x=1
    • D. dydx=y2x\frac{dy}{dx}=\frac{y^2}{x}

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