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Unformatted text preview: 74 Economic Dynamics In particular, we are assuming that y is a function of t , y ( t ). Then we employ the dsolve command by using dsolve(diff(y(t),t)=f(y(t),t),y(t)); Note a number of aspects of this instruction: (1) The equation utilises diff( y ( t ), t ) to denote dy / dt (2) The function f ( y ( t ) , t ) may or may not be independent of t (3) y ( t ) is written in the equation rather than simply y (4) The second term, y ( t ), is indicating what is being solved for and that t is the independent variable. It is possible to first define the differential equation and use the designation in the dsolve command. Thus Eq:=diff(y(t),t); dsolve(Eq,y(t)); If Maple can solve the differential equation then this is provided in the output. If Maple can find no solution, then the programme simply gives a blank output. The user does not need to know what algorithm is being used to solve the differential equation. What matters is whether a solution can be found. What is important to understand, however, is that a first-order differential equation (as we are discussing...
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- Fall '11