anonymous
  • anonymous
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)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
So I already drew a slope field. However, I am having trouble determining what part A here is asking?
Loser66
  • Loser66
From given equation, we have particular solution is \(y=e^{x^2/4}\) right? , the graph of it is |dw:1435151131722:dw|
Loser66
  • Loser66
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?

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Loser66
  • Loser66
in other words, f(0.2)> f(0) because the graph of \(e^{positive~number}\) is increasing.
anonymous
  • anonymous
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?
anonymous
  • anonymous
@Loser66
Loser66
  • Loser66
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)
anonymous
  • anonymous
Awesome! Thanks so much!
Loser66
  • Loser66
np
dan815
  • dan815
baby

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