Solve these differential equations to see how a minus sign can
change the answer
Match the descriptions of physical processes to these differential
Look at the advanced way of viewing sin and cos through their power series.
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 $m$th order with respect to $[A]$ if it satisfies a rate equation of the following type
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?