Find the value of the number LaTeX: a a such that the families of curves LaTeX: y=\left(x+c\right)^{-1} y = ( x + c ) − 1 and LaTeX: y\:=\:a\le​ft(x\:+\:k​\right)^{\​frac{1}{3}​} y = a ( x + k ) 1 3 are orthogonal trajectories.

Find the value of the number a such that the families of curves y=(x+c)−1and y=a(x+k)13 are orthogonal trajectories.

im trying to write htis on matlab to have it solved can you help me

[Mauricio Alvarez]

the y=a(x+k)^1/3 thats the second y equation thats incorrect on the top

[Mauricio Alvarez]

then the first is supposed to be y=(x+c)^-1

[Walter Roberson]

Find the value of the number a such that families of curves and are othogonal trajectories

Answer 1

[Pranav Verma]

Hi Mauricio,

As per my understanding, you intend to solve the above mentioned system of equations pertaining to the specified condition of trajectories being orthogonal. I'd suggest using the diff and solve function in MATLAB for achieving the above task.

Please refer to syms documentation also to use diff and solve.

Also refer to the below discussions on the same lines:

https://www.mathworks.com/matlabcentral/answers/512447-orthogonal-trajectories-in-matlab

https://www.mathworks.com/matlabcentral/answers/559403-find-the-value-of-a?s_tid=answers_rc1-1_p1_Topic

Thanks