the method used is to find what's known as an integrating factor. Integrating factor - Wikipedia, the free encyclopedia
Hi, I am trying to solve an assignment in chemistry which involves an ODE. The equation is:
where k_{a}, k_{b}, and [A]_{0 }are all constants.
My book provides a solution for equations of the form:
as
I plugged this in for my case and the correct answer came out. For future reference, what method can I look up to solve an equation like this, or how is it actually classified? I think it is nonlinear?
Thank you!
the method used is to find what's known as an integrating factor. Integrating factor - Wikipedia, the free encyclopedia
Another method: since this is a linear equation, you can separate it into a "homogeneous" part, which is easy to solve since it is "separable": . Find the general solution to that and add any one solution to the entire equation. And since the equation has constant coefficients, a function of the form should work. Put that into the equation and see what A must be in order that this must satisfy the equation.
Thanks for the help to both of you!
One question: HallsofIvy mentions that the equation is separable into [tex]\frac{d[I]}{I}=-k_{b}dt[\tex]
but I thought it wasn't separable because of the exponential term on the right-hand side of the original equation? Can you just ignore that term, since it doesn't seem to appear in HallsofIvy's homogeneous equation?
I also wasn't sure if it was linear because (at least in Wikipedia) a linear equation has all unknown functions and their derivatives to the first power, but I had a function f(t) that was an exponential function.
Hi,
Integrating factor will solve this. Try this out at once.
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I did NOT say that the original equation was "separable". I said that the "associated homogeneous equation,
was separable.
When Wikipedia refers to "unknown functions" here, it is referring to the function, I, that you are trying to solve for. Any other function is a "known" function.