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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.
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.
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???.
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 · The curves defined by Equation \ref{eq:4.5.19} are integral curves of Equation \ref{eq:4.5.22}, and the integral curves of \[y'={2xy\over x^2-y^2} \nonumber \] are orthogonal trajectories of the family Equation \ref{eq:4.5.19}.
13 kwi 2012 · Steps to find orthogonal trajectory. let f (x,y,c)=0 be the equation of the family of curves, where c is an arbitrary constant. Differentiate the given equation with respect to x and then eliminate c. replace by. Solve the obtained differential equation. You will get the required orthogonal trajectory. Category:
