For equation below:
$(t+1) \, dx=4(x+4) \, dt$
After separation I ended up with:
$(x+4)dx = \frac 4{t+1}dt $
Resulting in:
$\int x+4 \,dx = 4 \int \frac 1{t+1} \,dt$
So:
$\frac 12 x^2 + 4x + C = 4\ln(t+1) + C$
Now I have to express this as $x(t)$ and I have no clue how to. Also I am not sure if I did the above steps correctly. Any help will be appriciated!
UPDATE
As gerry pointed my mistake now I have:
$ \int \frac {1}{x+4}\,dx = 4\int \frac{1}{t+1}\,dt $
Then:
$ \ln(x+4) = 4 \ln(t+1) + C$
Still not able to express this as x(t)...how to?!