Question

Solve the differential equation:

x(1+y^2)dx+y(1+x^2)dy=0

The professor gave this as the answer:

1+y^2 = C^2 / (1+x^2)

I got:

1+y^2= e^(2C) / (1+x^2)

The only difference is the numerator on the right side. I tried the problem several times and I still couldn't get the numerator to become C^2. I would like to know which of us is right.

Answer 1

I think both of you are correct, but it is more proper to just us C rather than anything else because C^2 is just also equal to C or e^2C is just equal to C right?

Answer 2

Yeah, I understood that. I usually just do C on the arbitrary constants but on this particular problem, the professor was more specific.

Answer 3

actually, If I am to answer that question, my answer would have +C

Answer 4

My classmate also got e^2C and not C^2

Answer 5

ok, let me check again

Answer 6

ok

Answer 7

after integration, where did you put +C?

Answer 8

right side

Answer 9

we got the answer. I don't know how did your prof arrive to C^2

Answer 10

you got e^2C too?

Answer 11

ya

Answer 12

Well. I guess that makes the professor wrong...

Answer 13

Hey thanks for the help man.

Answer 14

haha. there's no way that you're going to have a C^2 with that equation.

Answer 15

I know right