Search results
30 cze 2023 · If you know the equation of one family of curves, you can find the orthogonal trajectories by finding the solution to the differential equation that describes the orthogonal family. This typically involves taking the derivative of the given equation, negating it, and finding the reciprocal to determine the slope of the orthogonal trajectories.
20 sty 2019 · Find the orthogonal trajectories to the family of curves. ???y=kx??? We always start by using implicit differentiation to take the derivative of both sides, and then we’ll solve for ???dy/dx???.
11 mar 2017 · My textbook, George F. Simmons' Differential Equations with Applications and Historical Notes, asks to find the orthogonal trajectory of the family of curves $r = 2Ccos(\theta)$ where C is a parameter.
29 sty 2018 · Our method of finding the orthogonal trajectories of a given family of curves is therefore as follows: first, find the differential equation of the family; next, replace d y= d x by d x= d y to obtain the differential equation of the orthogonal trajectories; and finally, solve this new
Below we describe an easier algorithm for finding orthogonal trajectories \(f\left( {x,y} \right) = C\) of the given family of curves \(g\left( {x,y} \right) = C\) using only ordinary differential equations. The algorithm includes the following steps:
7 sty 2020 · Step 1. Find a differential equation \[y'=f(x,y) \nonumber \] for the given family. Step 2. Solve the differential equation \[y'=-{1\over f(x,y)} \nonumber \] to find the orthogonal trajectories.
A procedure for finding a family of orthogonal trajectories G(x,y,K) = 0 for a given family of curves F(x,y,C) = 0 is as follows: Step 1. Determine the differential equation for the given family F(x,y,C)=0. Step 2. Replace y0 in that equation by −1/y0; the resulting equation is the differential equation for the family of orthogonal ...
