Main Question or Discussion Point
i got a book on differential equations that says a shortcut to solving the general differential equation f'(x)+p(x)f(x)=g(x) is to take the antiderivative of g(x) dx times exp(-p(x) dx times x) to solve for f(x) where dx represents the functions antiderivative. (i kno its supposed to represent the infinitesml area under part of a curve and i i were proper id write it as an improper integral. some unhelpful guy on yahoo answer pointed this out.) and yes, they explained how it worked. anyway, i was watching a tutorial on the schrodinger equation and i believe solving for the T(t) component of the wavefunction came down to the equation T'(t)+iE/(h-bar)T(t)=0. in this case p would be iE/(h-bar) and g=0 which i understand are constants. they said that the solution is T(t)=e^iEt/(h-bar). but i dont understand how the process i learned applies. if somebody could explain the process used thatd be great. im pretty sure i just got lost and i hope my question is clear.