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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)
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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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So I already drew a slope field. However, I am having trouble determining what part A here is asking?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3From given equation, we have particular solution is \(y=e^{x^2/4}\) right? , the graph of it is dw:1435151131722:dw

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3hence, 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?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3in other words, f(0.2)> f(0) because the graph of \(e^{positive~number}\) is increasing.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That 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?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3for 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
 one year ago
Best ResponseYou've already chosen the best response.0Awesome! Thanks so much!
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