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

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Exact differential equations

Exact differential equations

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

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Exact differential equations

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- [Instructor] So far you have learned how to solve linear and separable first order differential equations. But what do you do if the equation you are working with is not in either of those forms? In this video, you'll take a look at another type of non-linear differential equations, exact differential equations. A first order differential equation is said to be exact if it could be written in the form of capital M of x, y multiply by dx plus capital N of x, y multiply by dy equals 0. Note that capital M of x, y and capital N of x, y are both functions of x and y. You may notice that this would be difficult to solve since the x and y variables are mixed throughout, making no easy way to separate them. This is where things start to get a bit tricky, since now you'll introduce the concept of partial derivatives. Remember, partial derivatives are when you take a derivative of a function that contains multiple variables with respect to just one of the variables. Hence why it is partial…

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