Integrating factor: Difference between revisions
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'''Integrating factor''' is a method to solve scalar [[Linear First Order ODE]]<nowiki/>s. | '''Integrating factor''' is a method to solve scalar [[Linear First Order ODE]]<nowiki/>s. It takes advantage of the product rule of derivatives | ||
Consider | <math>(\mu y)' = \mu' y + \mu y'</math> | ||
and attempts to move all y terms into the same differential order. | |||
= Procedure = | |||
Consider a linear first order ODE. | |||
<math>y' + p(t) y = g(t)</math> | <math>y' + p(t) y = g(t)</math> |
Revision as of 23:28, 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.
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.