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 2 years ago
Solve the following D.E.,
\[\frac{dy}{1+y^2}=\frac{dx}{1+x^2}\], obtaining the result in algebraic form
 2 years ago
Solve the following D.E., \[\frac{dy}{1+y^2}=\frac{dx}{1+x^2}\], obtaining the result in algebraic form

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

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

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

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

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

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

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

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1If 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)

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

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

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

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

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

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

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

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

ebbflo
 2 years ago
Best ResponseYou've already chosen the best response.0no, 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...

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

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

ebbflo
 2 years ago
Best ResponseYou've already chosen the best response.0as 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...

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

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

ebbflo
 2 years ago
Best ResponseYou've already chosen the best response.0I 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

myininaya
 2 years ago
Best ResponseYou've already chosen the best response.1If 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

ebbflo
 2 years ago
Best ResponseYou've already chosen the best response.0yes 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...;)

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1differential 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

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

ebbflo
 2 years ago
Best ResponseYou've already chosen the best response.0I 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

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

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

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

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

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

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

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

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

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1implicit solutions are fine for DE's
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