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.
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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.