Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
ebbflo
Group Title
Solve the following D.E.,
\[\frac{dy}{1+y^2}=\frac{dx}{1+x^2}\], obtaining the result in algebraic form
 2 years ago
 2 years ago
ebbflo Group Title
Solve the following D.E., \[\frac{dy}{1+y^2}=\frac{dx}{1+x^2}\], obtaining the result in algebraic form
 2 years ago
 2 years ago

This Question is Closed

ebbflo Group TitleBest ResponseYou've already chosen the best response.0
the solution given by the text is \[y=x+C(1+xy)\]
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
i believe you should cross multiply first \[(1 + x^2)dy  (1+y^2)dx = 0\]
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
You just integrate both sides of that equation you have @ebbflo
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
You already have the variables separated
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.1
\[\int \frac{1}{1+z^2}\text dz=\arctan z+c\]
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Is your trouble writing it as an algebraic expression?
 2 years ago

ebbflo Group TitleBest ResponseYou've already chosen the best response.0
I see all of your points and have tried those methods but do not obtain the given answer....
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
If so.. Don't forget you only need one constant (and just put it on one side of your equation) Remember the inverse of tan inverse which is tan lol also remember the formula tan(a+b)=(tan(a)+tan(b))/(1tan(a)*tan(b)) Then remember that tan(constant) is still a constant)
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Remember @ebbflo it does say write as an algebraic expression.
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
You get trigonometric expression right after integration
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
You want to transform that to an algebraic one using the hint I just gave you
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Also recall tan(arctan(p))=p
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
You will use that too
 2 years ago

ebbflo Group TitleBest ResponseYou've already chosen the best response.0
thanks, I understand all the points you have made
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
What about the solution? Have you got the desired solution?
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Or do you need more help?
 2 years ago

ebbflo Group TitleBest ResponseYou've already chosen the best response.0
no, got it, i had the solution, just don't quite understand "why" the book's solution is written in the form it is... the first copyright is 1943, maybe its a style thing...
 2 years ago

ebbflo Group TitleBest ResponseYou've already chosen the best response.0
@myininaya , you can use Latex so that your math text is more clear
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
That one formula is a trig formula The expansion for tan(a+b) let me know if you need anything else
 2 years ago

ebbflo Group TitleBest ResponseYou've already chosen the best response.0
as i said, I had an equivalent solution, I was just curious as to why the book chose to write the solution in the form it did...
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Was your form algebraic?
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Can you write what you have?
 2 years ago

ebbflo Group TitleBest ResponseYou've already chosen the best response.0
I have the solution given, I think the book just wanted a form with one arbitrary constant, i generally don't like my solutions to have "y" on the LHS and RHS when it is not absolutely necessary...it was really ore of a "style" question, sorry I should have specified
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
If the equation can be written in the form the book gives, then your answer is right I got the same answer your book got I wrote it in a different form but it is still correct
 2 years ago

ebbflo Group TitleBest ResponseYou've already chosen the best response.0
yes I understand, thank you...as I said I was questioning the style, and now that I think of it it was probably that the books form only take a single line of text whereas mine did not...;)
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.1
differential equations will often have \(y\) on both sides of the solution, but that is alright. we were only trying to get rid of derivatives replace them with constants
 2 years ago

ebbflo Group TitleBest ResponseYou've already chosen the best response.0
@unkle agreed, but it is my preference not to do so when not necessary
 2 years ago

ebbflo Group TitleBest ResponseYou've already chosen the best response.0
I should have been more clear, I was not so much looking for "help" with the problem, but a different perspective on how another might write the solution
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.1
these are some solution to differential equations ,
 2 years ago

ebbflo Group TitleBest ResponseYou've already chosen the best response.0
in order to make a decision as to what a student may find more clear
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.1
your solution must include as many arbitrary constants as the order of the differential equation
 2 years ago

ebbflo Group TitleBest ResponseYou've already chosen the best response.0
exactly uncle, in those solution you provided, the "y" cannot be written explicitly in terms of "x", at least not in a single expression
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.1
well, it can but i just looks awful , these are 'neater'
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.1
looking at (e)
 2 years ago

ebbflo Group TitleBest ResponseYou've already chosen the best response.0
yeah that one can but what about (c)?
 2 years ago

ebbflo Group TitleBest ResponseYou've already chosen the best response.0
(e) more or less is already, not much more to do on that one...
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.1
i think it is clearer to write (c) like \[x = y^2(\ln y + c)\] i dont know why they chose the form they did
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.1
implicit solutions are fine for DE's
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.