Question

\text { 4. Consider the differential equation } \frac{d y}{d x}=2 x-y \text {. } (a) On the axes provided, sketch a slope field for the given differential equation at the six points indicated.

\text { (b) Find } \frac{d^{2} y}{d x^{2}} \text { in terms of } x \text { and } y \text {. Determine the concavity of all solution curves for the given differential } equation in Quadrant II. Give a reason for your answer. (c) Let y = f(x) be the particular solution to the differential equation with the initial condition f(2)= 3.Does f have a relative minimum, a relative maximum, or neither at x = 2 ? Justify your answer. (d) Find the values of the constants m and b for which y = mx + b is a solution to the differential equation.

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