I have the equation below:
$$(t^2 + 1)dx=(x+4)dt$$
Where $x(0) = 3$
I am trying to use separation of variables, and I end up here:
$$\ln(x+4)=\arctan(t)+C$$
Trying to simplify it more:
$$x=-4+\ln(\arctan(t)+C)$$
Is this correct? I think I should use $x(0) = 3$ to find value of the constant, how can I do that?
Thanks