Solved 1 Find The Family Of Orthogonal Trajectories For Chegg Step 1. solution: the given family of curves is y 3 3 x 2 y = c 1 …. (i) explanation: for orthogonal trajectories: replace d y d x by − d x d y. view the full answer step 2. unlock. step 3. unlock. Your solution’s ready to go! our expert help has broken down your problem into an easy to learn solution you can count on. question: find the orthogonal trajectories of the given family of curves. y = c 1 x 3x 4y = c 1 y = c 1x^2 y = (x c 1)^2 c 1x^2 y^2 = 1 2x^2 y^2 = c^2 1 y = c 1 r^ x 2x^2 y^2 = c^2 1 y = c 1e^ x y = e^c 1 x y^2.
Solved B Find The Orthogonal Trajectories For The Given Chegg Find the orthogonal trajectories to the family of curves. we always start by using implicit differentiation to take the derivative of both sides, and then we’ll solve for. , we’ll go back to the original equation and solve it for. , so the equation we just found represents the slope of the family everywhere. For the given family of curves, we can draw the orthogonal trajectories, that is another family of curves f (x, y) = c that cross the given curves at right angles. for example, the orthogonal trajectory of the family of straight lines defined by the equation y = kx, where k is a parameter (the slope of the straight line), is any circle having. This is the family of orthogonal trajectories. university of houston math 3321 lecture 068 31. orthogonal trajectories. example: 1.find the orthogonal trajectories of the family of parabolas with vertical axis and vertex at the point (−1,3). an equation for this family of parabolas is (y−3) = k(x 1)2. Dx. dy. =f(x;y):(10) 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 dy=dxby dx=dy. to obtain the differential equation of the orthogonal trajectories; and finally, solve this new differential equation.
Solved Find The Orthogonal Trajectories Of The Family Of Chegg This is the family of orthogonal trajectories. university of houston math 3321 lecture 068 31. orthogonal trajectories. example: 1.find the orthogonal trajectories of the family of parabolas with vertical axis and vertex at the point (−1,3). an equation for this family of parabolas is (y−3) = k(x 1)2. Dx. dy. =f(x;y):(10) 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 dy=dxby dx=dy. to obtain the differential equation of the orthogonal trajectories; and finally, solve this new differential equation. 3.find the orthogonal trajectories of the family of curves y2 = kx3: (an orthogonal trajectory of a family of curves is a curve that intersects each curve of the family orthogonally, that is, at right angles) sketch several members of each family on a common graph (feel free to use mathematica or any other graphing utility to help create this. Trajectory of the other family, then the two families are said to be 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.
Solved Find The Orthogonal Trajectories Of The Given Family Chegg 3.find the orthogonal trajectories of the family of curves y2 = kx3: (an orthogonal trajectory of a family of curves is a curve that intersects each curve of the family orthogonally, that is, at right angles) sketch several members of each family on a common graph (feel free to use mathematica or any other graphing utility to help create this. Trajectory of the other family, then the two families are said to be 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.
Comments are closed.