Why does integrating factor work

Of course integrating factors are there to help solving the original equation and we better check our solutions. If we find a solution which makes the integration factor zero, then we can check it in our original differential equation and in case that it does not satisfy our equation we disregard it.

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Ask Question. Asked 3 years, 1 month ago. Active 3 years, 1 month ago. Viewed times. Remember the names of the variables in an equation can be anything, and so, just work with whichever letters the problem requires.

If you have a variable named y this will usually be the dependent variable and therefore it doesn't matter the name of the other one, that will be the independent variable the one you write first.

For example, in the problem for example 2 the variables where t,y meaning t was the independent variable t could be written in terms of y. For further reading on the integrating factor method we suggest you to take a look at this tutorial module on how to solve first order linear differential equations through this technique. Back to Course Index. You can still navigate around the site and check out our free content, but some functionality, such as sign up, will not work.

If you do have javascript enabled there may have been a loading error; try refreshing your browser. That's the lesson. That's the last lesson. Let's keep going. Play next lesson or Practice this topic. Start now and get better math marks! Intro Lesson. Lesson: 1. Lesson: 2. Intro Learn Practice. Integrating Factor Technique Linear equations method of integrating factors For the past sections we have been studying ways to solve linear first order differential equations with methods such as separable equations, or exact equations, but remember these two methods only work under certain ideal conditions.

Just as before, we start with a differential equation of the form: Equation 1: General form of first order differential equation. Equation 2: Condition for an exact differential equation. Equation 3: Example of proportionality consistency in math equalities.

Example 1: Solve the given differential equation. Example 1 a : identifying M and N and checking if equation is exact. Example 1 b : Applying the integrating factor and identifying the new M and N. Example 1 c : Setting the equation as exact to find the integrating factor. Example 1 d : Finding the integrating factor. Example 1 e : Rewriting the differential equation with the value found for the integrating factor.

Example 1 f : Integrating N to find Psi. Example 1 g : Finding function f x. Example 1 h : Finding the final general solution Psi. Example 2: Solve the given differential equation. Example 2 a : identifying M and N and checking if equation is exact. Example 2 b : Applying the integrating factor and identifying the new M and N. Example 2 c : Setting the equation as exact to find the integrating factor.

That is,. Exactness of this equation means. Previous Exact Equations. Next Separable Equations. Removing book from your Reading List will also remove any bookmarked pages associated with this title. Are you sure you want to remove bookConfirmation and any corresponding bookmarks? My Preferences My Reading List.