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dx / dt = 3*x + y

dy / dt = -y

As for solving this, here is what I've got so far:

Since dy/dt is separable, I found that dy / y = -dt, integrated, and solved explicitly for y:

y = Ce^-t

I then plugged Ce^-t for y in the dx / dt portion of the system and found that:

dx/dt - (3*x) = Ce^-t

Then used Integrating Factor method, found u(t) = e^(-3t), multiplied to both sides and integrated and solved explicitly for x.

x = (-1/3)C + Ce^(3t)

For the second portion of the question, it asks to verify that the solution is correct.

To do that, I plugged in the x and y solutions from part 1, as well as took derivatives of x and y and plugged them in as well.

dy / dt = -y, -Ce^-t = -Ce^-t

However, the problem I am having is that when I plug in for the dx / dt equation, I get down to t = ln1 = 0.

I don't understand if this is wrong or what, as the y solution works but the x one doesn't seem to come to any reasonable conclusion.

Any help in understanding these results, or in finding mistakes would be much appreciated.

-twiztidmxcn

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# Homework Help: Differential Equations - First Order Systems

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