First-order linear equations. A first-order linear equation has the general form If the equation is called homogeneous ; otherwise it is called inhomogeneous . For example, is a linear equation, and an inhomogeneous one, since it can be written as.
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
If the equation is called homogeneous; otherwise
it is called inhomogeneous.
inhomogeneous one, since it can be written as
we multiply the equation by a suitable function I(x):
If the factor I(x) is chosen such that
then equation (2) becomes
which can be solved by
that equation (3) holds true:
This is equivalent to
which is a separable equation for I(x). Its solution is
factor of equation (1).
Multiplying I(x) to the equation, we get
variable and y as independent variable: