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)

Question

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 · Answer

So I already drew a slope field. However, I am having trouble determining what part A here is asking?

loser66 · Answer

From given equation, we have particular solution is $y=e^{x^2/4}$ right? , the graph of it is |dw:1435151131722:dw|

loser66 · Answer

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?

loser66 · Answer

in other words, f(0.2)> f(0) because the graph of $e^{positive~number}$ is increasing.

anonymous · Answer

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?