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

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Solving differential equations using Laplace transforms

Solving differential equations using Laplace transforms

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

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Solving differential equations using Laplace transforms

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- [Lecturer] So far, you have learned what Laplace transforms are, how to calculate them, what their various properties are, and how to even calculate their inverses. In this video, you'll put all of that together by using Laplace transforms to calculate differential equations. The reason why solving differential equations with Laplace transforms is helpful is because it converts them into algebraic equations that are fairly straightforward to solve. You will notice the differentiation property will be heavily used throughout the calculations due to the nature of the equations being worked on containing derivatives. Let's review the steps of how to calculate differential equations using Laplace transforms. Step one, you will determine and apply the Laplace transform to both sides of your differential equation. Step two, you will substitute initial conditions into your result. Step three, you will solve for the now algebraic equation for your frequency function capital F of s. Note…

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