From the course: Complete Guide to Differential Equations Foundations for Data Science
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Curves
- [Instructor] I have one more practical application to share with you for first order differential equations. This time, let's see how you can apply differential equations with curves such as a particle moving on a curve. Let's dive in. Curve problems tend to involve the relationship between a curve's particle position, velocity, and acceleration along the curve. You'll model the motion of the particle with respect to time, using one or more differential equations. The position of the particle can be expressed parametrically, where the position along a curve is defined by the coordinates X of T and Y of T as functions of time T. The steps you will use to solve a particle moving on a curve is, step one, establish the equation for the curve, either by linear or parametric equations. Step two, write the velocity components by taking the first derivatives of the position with respect to time T. And finally, for step three, form a differential equation, using Newton's second law motion…
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