From the course: Complete Guide to Differential Equations Foundations for Data Science

Unlock this course with a free trial

Join today to access over 25,300 courses taught by industry experts.

Variation of parameters

Variation of parameters

From the course: Complete Guide to Differential Equations Foundations for Data Science

Start my 1-month free trial Buy for my team

Variation of parameters

“

- [Instructor] In the previous video, you learned how to use the undetermined coefficients technique to solve second order nonhomogeneous differential equations. But what do you do if the equation you're working with doesn't have the nice format required for undetermined coefficients? This is where variation of parameters becomes helpful. The variation of parameters method helps you gather a particular solution to add to your general solution to a second order nonhomogeneous differential equation. Instead of having to make an initial guess of the form of your particular solution, you'll be finding the solution to two unknown functions substituted into your equation. Let's say you are working with the second order nonhomogeneous differential equation with the form of P of X multiplied by Y double prime, plus Q of X multiplied by Y prime, plus R of X multiplied by Y equals capital F of X. Note that capital F of X is a function that does not equal zero, hence making it nonhomogeneous…

Contents