Derivatives & Differential Equations
A first order homogeneous differential
equation involves only the first derivative
of a function and the function itself, with constants only as multipliers. The
equation is of the form
and can be solved by the
substitution
The
solution which fits a specific physical situation is obtained by substituting
the solution into the equation and evaluating the various constants by forcing
the solution to fit the physical boundary
conditions of the problem at hand. Substituting gives