Question: Consider the first order ODE dy = = f(x, y) = x + y. dx (a) Sketch the slope field in the x, y-plane.

Consider the first order ODE dy = = f(x, y) = x

Consider the first order ODE dy = = f(x, y) = x + y. dx (a) Sketch the slope field in the x, y-plane. (b) One of the solution curves is a straight line. Find the equation of this line. [Hint: Suppose that y = mx + b for some constants m and b. Then we have dy m = = x+y=x+mx+b. dx Hence the equation m = x + mx + b holds for any value of x. Use this to solve for m and b.]

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