Solve y'=1+x^2+y^2+x^2y^2: Step-by-Step Solution

[jrodss]

1. Give the general solution for the following problem

2. y'=1+x^2+y^2+x^2y^2

3. I have attempted to separate the equation and came up with the following:
y'=1+y^2+x^2(1+y^2) from there I ended up with (y'-y^2-1)/(1+y^2)=x^2
I am stuck on what step to take next. I am sure I am just missing something simple.

 

[blerg]

So you want to get y'=q(y)*p(x) from your original equation. How can you do that?

 

[jrodss]

Thanks, i got it, i knew i was forgetting something small, it factors out to (x^2+1)(y^2+1) Makes the whole thing a lot easier.

Thanks again for the help.

 

[Дьявол]

What is general solution?

 

[jrodss]

The general solution I came up with is y=tan(x³/3+x+C)