dx/dt=-ax
dy/dt=ax-by
where a and b are constants. Solve this system subject to x(0)=x_0 (x "not") and y(0)=y_0 (y "not")
Is it possible to substitute -dx/dt into equation 2 or do I have to solve equation one first to find the solution of x first?
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dx/dt=-ax
dy/dt=ax-by
where a and b are constants. Solve this system subject to x(0)=x_0 (x "not") and y(0)=y_0 (y "not")
Is it possible to substitute -dx/dt into equation 2 or do I have to solve equation one first to find the solution of x first?
solve the first DE for x (it is a separable DE), and plug that into the second DE.Quote:
Originally Posted by daskywalker
(and it is x- and y- naught, as in zero)
ok so for the first DE I got x=Ke^-at where K is the constant e^c (from integration) How do I substitute the condition x(0)=x_0? Or do I substitute the whole expression into equation 2?
Quote:
Originally Posted by daskywalker
means, when
We have. applying the initial condition, we see that
Thus,. Plug this expression in the second equation