# Differential Question

1. Jun 30, 2010

### beetle2

1. The problem statement, all variables and given/known data

Hi Guys,
I've got a couple of examples of de's in my lecture notes. one is:
$y'=1+x^2$
which has a general solution of $y= x+\frac{x^3}{3} + c$
which i I understand they have taken the integral wrt $x$

the second is

$y'=1+y^2$ which has a general solution of $y=$tan$(x+c)$

Can some one please explain to me how that got the second solution?

2. Jun 30, 2010

### Staff: Mentor

Both problems can be done by the technique of separation of variables.

For the first, you have
dy/dx = 1 + x^2
==> dy = (1 + x^2)dx
Integrate both sides to get what you already have shown.

For the second, you have
dy/dx = 1 + y^2
==> dy/(1 + y^2) = dx
Now integrate both sides to get
arctan(y) = x + C ==> y = tan(x + C).

3. Jun 30, 2010

### beetle2

Thanks mate I had forgoten about separation of variables.
I was integrating both sides wrt x in the second example.

4. Jun 30, 2010

### Staff: Mentor

And good luck with that!