involving differential equations
will integration by separation by variables and integration by integration factor give the same answer??
cheers to all who respond
In those cases where both methods are applicable, both methods will yield the same result. Not every DE is separable, and not every DE is first-order linear (the requirement for being able to use the integrating factor method).
I should mention one thing: the way the arbitrary constant looks might vary from one method to the other. But it should behave mathematically the same way (e.g., it's multiplying something, or it's added to something).
thank you...i was unsure whether i had to use integration by parts in one of my equations..although i have got the same result by both..so in this case i do not need to.
or is integration by parts only applicable on in the RL and RC electrical circuits.
thanks
Integration by parts is not the same idea as separation of variables, nor is it the same concept as the integrating factor.
In RL and RC circuits, you use whatever methods you can! They're first-order DE's, so there's the possibility of a bunch of methods being available to you, especially if the DE is linear. You might use integration by parts in there somewhere, but it would be in the context of a higher-up method such as separation of variables or the integrating factor method. Most of the time, you can't just solve a DE by integrating by parts.or is integration by parts only applicable on in the RL and RC electrical circuits.