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anonymous

  • one year ago

Consider the differential equation dy/dx= (xy)/2. A. let y=f(x) be the particular solution to the given differential equation with the initial condition. Based on your slope field, how does the value of f(0.2) compare to f(0)? Justify this. B. find the particular solution y=f(x) to the given differential equation with the initial condition f(0)=3. Use your solution to find f(0.2)

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  1. anonymous
    • one year ago
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    So I already drew a slope field. However, I am having trouble determining what part A here is asking?

  2. Loser66
    • one year ago
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    From given equation, we have particular solution is \(y=e^{x^2/4}\) right? , the graph of it is |dw:1435151131722:dw|

  3. Loser66
    • one year ago
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    hence, compare the steep of the graph, at x =0.2, f(0.2) will be a little bit steeper than it is at x =0, ok?

  4. Loser66
    • one year ago
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    in other words, f(0.2)> f(0) because the graph of \(e^{positive~number}\) is increasing.

  5. anonymous
    • one year ago
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    That makes sense! Thanks so much! Now, when it comes to part B with f(0)=3, how do I determine what f(x) should be?

  6. anonymous
    • one year ago
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    @Loser66

  7. Loser66
    • one year ago
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    for part b) \(y = e^{x^2/4}+C\) replace initial condition x =0 , y = 2 to find C then plug back to find f(0.2)

  8. anonymous
    • one year ago
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    Awesome! Thanks so much!

  9. Loser66
    • one year ago
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    np

  10. dan815
    • one year ago
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    baby

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