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

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Superposition

Superposition

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

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Superposition

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- [Instructor] In the previous video, you worked with the characteristic equation to solve constant coefficient, homogenous, second-order differential equations. In this video, you will focus on a more generalized technique to solve linear differential equations. Let's get started. The principle of superposition states, for a linear homogeneous differential equation, any linear combination of solutions is also a solution. This holds true because linear differential equations satisfy the property of linearity. For a nonhomogeneous differential equation, the general solution is the sum of the general solution of the homogeneous version of the equation and a particular solution of the nonhomogeneous equation. Note the particular solution helps account for that nonhomogeneous term. Like I mentioned before, you can use this technique with linear differential equations only. The general solution for the homogeneous version of the superposition formula is given by y of x equals C1 multiplied…

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