Ok, I told my differential equations class to solve:
with initial condition
This is straight forward right? I expected the “good” student to separate the variables:
and integrate; the left hand side can be done by an easy integration; one can use partial fractions but I allow them to use calculators that have symbolic calculus operations on it.
Now of course, you had the bad student mistake: integrating the right hand side with respect to :
but you will always have some clueless students.
But what surprised me was this: some students used the Bernoulli change of variable method:
which leads to and then setting which leads to:
and that gives which has solution and then
Those who did this got it mostly right, though most made algebraic errors along the way.
So I am glad that they knew the more advanced technique but why use it here? 🙂