Why e-Integral Factor Omits Constant Integral?

[bennyska]

whenever i see that integrating factor for solving a linear differential equation with
e^{int. p(x) dx} and then multiplied out in the equation, there seems to be no constant. i tried solving an equation with it the other day, and got an incorrect solution because of it (i think. at least i got a correct solution when i neglected it).
why is this?

 

[torquil]

Check this example:

http://en.wikipedia.org/wiki/Examples_of_differential_equations

The section "Non-separable first-order linear ordinary differential equations". An arbitrary additive term in the integral in the exponential, can be written as a constant prefactor on \mu. Since the whole equation is multiplied by \mu, this is irrelevant for finding the solution.

And you can se in the explicit expression for the final solution y that you have the freedom to redefine \mu by multiplying it ba any nonzero number, since the parameter C is not determined.

Torquil

 

[bennyska]

cool, thanks.