Consider the differential equation given by dy/dx = xy/2.

Question

A. Let y=f(x) be the particular solution to the given differential equation with the initial condition. Based on the slope field, how does the value of f(0.2) compare to f(0)? Justify your answer.

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).

Answer 1

dy/dx = xy/2
dy/y = x/2 dx
ln y = 1/4 x^2 + c
y = c e^(x^2/4)

Answer 2

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