Question: Consider the linear first order differential equation and 4 y 4 . (a) Calculate the gradients at integer points ( x,y )

Consider the linear first order differential equation

dy -4 dy -4                                                                                                                                                                       and − 4 ≤ y ≤ 4.

(a) Calculate the gradients at integer points (x,y) in the x,y-plane and present your results in a table.

 (b) Use your results from (a) to plot the gradient field of the given differential equation. Do not plot the isoclines.

 (c) Plot integral curves passing through the points (0,−2), (0,0) and (1,2).

dy -4 dy -4

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