linear differential equation of first order
An ordinary linear differential equation of first order has the form
For finding the solution of (1), we may seek a function which is product of two functions:
One of these two can be chosen freely; the other is determined according to (1).
We substitute (2) and the derivative in (1), getting , or
If we chose the function such that
this condition may be written
Integrating here both sides gives or
Considering the chosen property of in (3), this equation can be written
So we have obtained the solution
of the given differential equation (1).
|Title||linear differential equation of first order|
|Date of creation||2013-03-22 16:32:09|
|Last modified on||2013-03-22 16:32:09|
|Last modified by||pahio (2872)|
|Synonym||linear ordinary differential equation of first order|