solving Differential Equation

I have the formula below:

$$(t^2 + 1)dx=(x+4)dt$$

Where $x(0) = 3$

I am attempting to make use of splitting up of variables, and also I wind up here:

$$\ln(x+4)=\arctan(t)+C$$

Trying to streamline it more:

$$x=-4+\ln(\arctan(t)+C)$$

Is this proper? I assume I should make use of $x(0) = 3$ to find value of the constant, just how can I do that?

Many thanks