Orthogonal trajectories

[Bliman]

Hi, I am stuck on a few exercises and I don't know what I am doing wrong.
The problem states. Find the orthogonal trajectories of the given family of curves.
I am stuck on this one.
x^2-y^2=cx
I will upload my solution and work.
Can anyone tell me what I am doing wrong? Thank you

CCF-000028 hosted at ImgBB

Image CCF-000028 hosted in ImgBB

ibb.co

CCF-000029 hosted at ImgBB

Image CCF-000029 hosted in ImgBB

ibb.co

 

[blamocur]

I could not find any errors in your post, so I've plotted both answers: yours and the one from the book. I've attached both plots, where the original family is in blue, your result in cyan and the book's in magenta -- you be the judge

 

[blamocur]

I could not find any errors in your post, so I've plotted both answers: yours and the one from the book. I've attached both plots, where the original family is in blue, your result in cyan and the book's in magenta -- you be the judge

... but the book's answer looks better when the original family is defined by [imath]x^2 + y^2 = cx[/imath].

 

[Bliman]

I could not find any errors in your post, so I've plotted both answers: yours and the one from the book. I've attached both plots, where the original family is in blue, your result in cyan and the book's in magenta -- you be the judge

Oh thank you. So I got it right. It is such a nuisance when the book answers are wrong.
Can you tell me what program you used for the curves?
And thanks again.

 

[blamocur]

Oh thank you. So I got it right. It is such a nuisance when the book answers are wrong.
Can you tell me what program you used for the curves?
And thanks again.

I used contour plotting in matplotlib, which is a Python/NumPy library for graphics.

BTW, are you sure about the original problem statement? I.e., is it actually x^2 - y^2=cx and not x^2 + y^2=cx ?

 

[Bliman]

I used contour plotting in matplotlib, which is a Python/NumPy library for graphics.

BTW, are you sure about the original problem statement? I.e., is it actually x^2 - y^2=cx and not x^2 + y^2=cx ?

Thank you. Yeah I am sure. It is in the book Ordinary differential equations with applications by Larry C Andrews.
Excercises 3.2 problem 7.