5.18 Differential equations

5.18 Differential equations Quiz

IB Maths: Analysis and Approaches HL: Quiz

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

    • A. 2ln⁡x2\ln x
    • B. x2x^{2}
    • C. e2xe^{2x}
    • D. 1x2\frac{1}{x^{2}}

  2. 2. For dydx=y\frac{dy}{dx}=y with y(0)=1y(0)=1, one Euler step with h=0.5h=0.5 gives:

    • A. 1.51.5
    • B. 1.251.25
    • C. 22
    • D. 1.651.65

  3. 3. Which differential equation is homogeneous?

    • A. dydx=x+y2\frac{dy}{dx}=x+y^{2}
    • B. dydx=yx+x\frac{dy}{dx}=\frac yx+x
    • C. dydx=y−xy+x\frac{dy}{dx}=\frac{y-x}{y+x}
    • D. dydx=xy\frac{dy}{dx}=xy

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

    • A. y=ln⁡x+cy=\ln x+c
    • B. y=−e−yx+cy=-e^{-y}x+c
    • C. y=ex+cy=e^{x}+c
    • D. y=ln⁡(x+c)y=\ln(x+c)

  5. 5. A population satisfies dNdt=0.001N(400−N)\frac{dN}{dt}=0.001N(400-N) with N(0)=50N(0)=50. What happens to NN in the long term?

    • A. N→200N\to200
    • B. N→400N\to400
    • C. N→∞N\to\infty
    • D. N→0N\to0

Quiz