Integrating factor: Difference between revisions

From Rice Wiki
No edit summary
No edit summary
Line 4: Line 4:


and attempts to move all y terms into the same differential order.
and attempts to move all y terms into the same differential order.
Note that [[Separation of variables]] is generally easier when both options are available.


= Procedure =
= Procedure =

Revision as of 23:30, 23 April 2024

Integrating factor is a method to solve scalar Linear First Order ODEs. It takes advantage of the product rule of derivatives

and attempts to move all y terms into the same differential order.

Note that Separation of variables is generally easier when both options are available.

Procedure

Consider a linear first order ODE.

We multiply bothsides by integrating factor such that the left hand side to be the exact derivative of a product. For this to work, we need

Applying the integrating factor, we have

From there, simple integration and algebra will solve the equation.