did you already solve this? i saw the "solved" tag above but i don't actually see that you solved your problem.
Question: For what values of and will be an integrating factor for the differential equation
The exact differential equation which results from multiplying by this integrating factor has solution where ___________________________.
Attempt at solving the question:
First I check to see whether either differential is exact (equal to each other), of course they are not.
The continue to solve and reach this point:
I should be able to factor something out, but i don't seem to find any, so am I doing the question wrong?
Actually, i did that because no one was responding. Anyways, I did figure out my integrating factor to be
I get to a point where after i multiplied both parts of the equation by the integrating factor and then i took the integral of the part of the equation and i get my F(x,y) which is . After wards i took the partial derivative with respect to y and got . I equate both equations and i get , which if i integrated k'(y), i would get C since. But my ans i entered was incorect.
you can actually find the integrating factor of the form the equation has it when for constants we have
it's a necessary and sufficient condition, so if it doesn't hold, don't waste your time.
on the other hand always compute and see its form, it would give ya an idea if you can find an integrating factor depending exclusively of or
here's a hint, multiply both sides by and apply the method to find the integrating factor you were asked to find.