Search results
30 cze 2023 · Step 1. Start with the equation of the given family of curves. This equation will typically involve a parameter (usually denoted by C or k) that differentiates one curve in the family from another. Step 2. Differentiate the given equation with respect to x (or y, depending on the function) to find the slope of the curve, dy/dx.
20 sty 2019 · Step-by-step example of how to find the orthogonal trajectories. Example. 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???.???(1)\frac{dy}{dx}=k(1)?????\frac{dy}{dx}=k???
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:
21 paź 2019 · Find the orthogonal trajectories of the family of curves given by $x^2 + y^2 + 2Cy =1$.
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
Understanding a family of curves and their trajectories Given a family of curves, like y=kxy=kx, we can choose different values for kk to write the equations of some of the curves in the...
In mathematics, an orthogonal trajectory is a curve which intersects any curve of a given pencil of (planar) curves orthogonally. For example, the orthogonal trajectories of a pencil of concentric circles are the lines through their common center (see diagram).
