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