Solve the system dx/dt = x with x(0) = Give your solution in real form. x1 = x 2

Question

Solve the system dx/dt = x with x(0) = Give your solution in real form. x1 = x 2 = [Note--you'll probably want to view the phase plotter at phase plotter (right click to open in a new window). Select the "integral curves utility" from the main menu. ] If y' = Ay is a differential equation, how would the solution curves behave? The solution curves would race towards zero and then veer away towards infinity. (Saddle) All of the solutions curves would converge towards 0. (Stable node) All of the solution curves would run away from 0. (Unstable node) The solution curves converge to different points.

Explanation / Answer

C.All of the solution curves would run away from 0. Given y' = Ay =>y will be an equation in power of e (which would run away from 0.)

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