The equation has an integrating factor that depends on .
I am trying to solve the following differential equation but cannot get a method that will work.
I have tried making it exact as well as various substitutions. All to no avail. I am thinking some sort of combination of variables might work, but I am stumped.
One way to get an integrating factor is to posit an integrating factor of the form Multiply through, take your partial derivatives, turn the crank, etc. The nice thing about doing it this way is that it takes care of a lot of situations in one fell swoop. It won't solve every first-order DE, not even all first-order DE's solvable by means of an integrating factor. But it will solve quite a few.Solving you'll obtain . In our case , verify that .