Separable differential equations

Separable differential equations Quiz

Spec H7–H8 · AQA A-Level Maths: Quiz

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5 questions, one answer each

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  1. 1. Which equation is separable?

    • A. dydx=x+y\frac{dy}{dx}=x+y
    • B. dydx=x2y\frac{dy}{dx}=x^2y
    • C. dydx=sin⁡(x+y)\frac{dy}{dx}=\sin(x+y)
    • D. dydx=x+y2\frac{dy}{dx}=x+y^2

  2. 2. The general solution of dydx=3y\frac{dy}{dx}=3y is

    • A. y=3x+Ay=3x+A
    • B. y=e3x+Ay=e^{3x}+A
    • C. y=3Aexy=3Ae^x
    • D. y=Ae3xy=Ae^{3x}

  3. 3. dydx=xy\frac{dy}{dx}=\frac{x}{y} with y=2y=2 when x=0x=0, y>0y>0. Which is correct?

    • A. y2=x2+4y^2=x^2+4
    • B. y2=x2+2y^2=x^2+2
    • C. y=x2+2y=x^2+2
    • D. y2=x2−4y^2=x^2-4

  4. 4. A particle has dvdt=−2v\frac{dv}{dt}=-2v and v=5v=5 at t=0t=0. Find vv when t=1t=1 (3 s.f.).

    • A. 33
    • B. 0.6770.677
    • C. −5.00-5.00
    • D. 0.1350.135

  5. 5. A model says P=100e0.2tP=100e^{0.2t} for a population. A sensible limitation is that

    • A. PP is always positive
    • B. tt is measured in years
    • C. P=100P=100 when t=0t=0
    • D. PP increases without limit, which is unrealistic as resources are finite

Quiz