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

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Linear differential equations

Linear differential equations

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

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Linear differential equations

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- [Instructor] In this video, you'll expand upon your knowledge of working with first-order differential equations by exploring linear first-order differential equations. You'll focus on learning what these equations are and how to solve them using the integrating factors method. Let's get started. A first-order differential equation is said to be linear if it could be written in the standard form of y prime plus p of x multiplied by y equals q of x. Linear differential equations must have their dependent variable y and its derivatives with a power no higher than one. Note that you can have a power of zero, meaning the function is a constant value, such as if you have the constant function of seven. You can classify your linear differential equation depending on what your q of x equals. If q of x equals zero, then it is what is called homogeneous, where there is no external force affecting the solution. If q of x is not equal to zero, then the equation is called nonhomogeneous, where…

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