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Economics Dynamics Problems 63

# Economics Dynamics Problems 63 - possible to solve fairly...

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Continuous dynamic systems 47 Figure 2.10. But equation (2.18) is just a particular example of a more general differential equation dx dt = g ( t ) f ( x ) (2.19) Any differential equation which can be written in terms of two distinct functions f ( x ) and g ( t ) is said to be a separable differential equation. Some examples are the following: (i) dx dt = 1 x 2 (ii) dx dt = x (2 x ) (iii) dx dt = ± 1 2 xt Our interest in these particular differential equations is because they are often
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Unformatted text preview: possible to solve fairly readily since we can write one side in terms of x and the other in terms of t . Thus, writing (2.19) in the form f ( x ) dx dt = g ( t ) we can then integrate both sides with respect to t ² f ( x ) dx dt dt = ² g ( t ) dt + c or F [ x ( t )] = ² g ( t ) dt + c...
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