Consider the differential equation given by $\dfrac{dy}{dx} = \dfrac{xy}{2}$. (a) On the axes provided, sketch a slope field for the given differential equation at the nine points indicated. (b) Let $y = f(x)$ be the particular solution to the given differential equation with the initial condition $f(0) = 3$. Use Euler's method starting at $x = 0$, with a step size of 0.1, to approximate $f(0.2)$. Show the work that leads to your answer. (c) Find the particular solution $y = f(x)$ to the given differential equation with the initial condition $f(0) = 3$. Use your solution to find $f(0.2)$.
Consider the differential equation given by $\dfrac{dy}{dx} = \dfrac{xy}{2}$.\\
(a) On the axes provided, sketch a slope field for the given differential equation at the nine points indicated.\\
(b) Let $y = f(x)$ be the particular solution to the given differential equation with the initial condition $f(0) = 3$. Use Euler's method starting at $x = 0$, with a step size of 0.1, to approximate $f(0.2)$. Show the work that leads to your answer.\\
(c) Find the particular solution $y = f(x)$ to the given differential equation with the initial condition $f(0) = 3$. Use your solution to find $f(0.2)$.