You did all 3 fine. One constant is as good as another.
I tried solving for the orthogonal trajectories of the following three families:
here are my solutions:
and my answers for the respective problems were:
But the answers from the book are, respectively:
What am I doing wrong or not understanding or how do I make my answers more consistent with the proper format as per in the book? Especially in the 2nd problem on my left hand side i got as opposed to the answer's left hand side which is please help me
He is changing the constant 'c' into 'a' on purpose? and if so then how do you know what you're suppose to change 'c' into?
I have a new set of roadblocks with this topic of orthogonal trajectories. Here are three problems that I tried to solve:
The first one I was able to solve however my answer differs from the answer in the book and I cannot find a way to how that they are both equal so either I or the book have the wrong answer, the second one I am stuck in a part where the equations suddenly seem to become quadratic and I do not know how to deal with this in differential equations, the third one I simply do not know how to solve the resulting differential equation after dy/dx has been replace with its negative reciprocal. Any help would be appreciated.