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Imagine that the rate of a chemical reaction only depends on the concentration of a single chemical A, with concentration denoted by [A]. The reaction is called mth order with respect to [A] if it satisfies a rate equation of the following type
-\frac{d[A]}{dt} =k[A]^m
This problem involves trying to find various solutions to rate equations from a purely mathematical perspective. As a rate equation is non-linear in [A] if m\neq 1 it is difficult to say how many different sorts of solution it might possess.
To begin with, can [A] =\lambda+\mu t ever be a solution to a rate equation? What would be the order of the reaction? What possible values could \lambda and \mu take?
Can [A]=(\lambda+\mu t)^n ever solve a rate equation when n is a positive whole number other than 1? A negative whole number? Zero?
What are the possibilities if n is not a whole number?
Which other solutions can you find to a rate equation?
Solve these differential equations to see how a minus sign can change the answer
Match the descriptions of physical processes to these differential equations.
Look at the advanced way of viewing sin and cos through their power series.