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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.
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???.
21 paź 2019 · Find the orthogonal trajectories of the family of curves given by $x^2 + y^2 + 2Cy =1$.
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}.
An orthogonal trajectory of a family of curves is a curve that intersects each curve of the family orthogonally—that is, at right angles. ORTHOGONAL TRAJECTORY Each member of the family y = mx of straight lines through the origin is an orthogonal trajectory of the family x2 + y2 = r2 of concentric circles with center the origin.
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