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Differential Equations: Orthogonal Trajectories: Example 1

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First published at 00:56 UTC on August 8th, 2018.

#mathematics
#calculus
#science

Math Easy Solutions

MES

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In this video I go over a recap on orthogonal trajectories as well as an example on how to go about solving for a family of orthogonal trajectories to the parabolas x = k*y^2, where k is a constant. The first step is to write the parabolas equation as a differential equation and solve for the derivative. Then, as proved in my earlier video, if a curve is perpendicular or orthogonal to another, then the slopes of the tangent line must be a negative reciprocal to the tangent line of the other curves. Thus from this fact we can obtain a second differential equation, which luckily is a separable equation, and can be solved resulting in a family of ellipses. This is a very useful example on the steps involved in determining the orthogonal trajectories, which are actually used a lot in physics and engineering applications such as electricity and fluid-dynamics!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhssPKzJnQRYh0guekA

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/differential-equations-orthogonal-trajectories-example-1

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