Seperable Differential Equations, Multiplicative Constant Confusion Help Clarify

[danerape]

I curiously never had a problem solving Seperable Equations in the Seperable Equations chapter of the Boyce/Diprima book. I am the kind of person who likes to do things the long way, and encountered a problem solving for an Integrating Factor(Linear ODE, NOT EXACT) the long proofy way. I tend not to use the (e^(INT)p(x)dx) formula. Formulas are too easy to forget.

In solving for the integrating factor, I came upon an easy seperable equation of course! I split this one up a little differently than usually, still correctly I think? I came up with an answer that differs from the formula approach.

Is the 1/3 absorbed by the constant or something?
PDF ATTACHED

Thanks,

Dane

 

[epenguin]

Yes you could say they are equal. I prefer to say they are the same thing - and if you wrote 15K₃ instead of K₁ it would the same thing. At this stage they are both arbitrary, in a sense they are not anything. When you make conform to an initial condition you will get the same result from either of them.