I have the following problem:
$$(t+2)dx=2x^2dt$$
First I divide both sides by $t+2$ to get: $$dx = \frac {2x^2}{t+2}\,dt $$ Then, divide by $2x^2$ to gey: $$\frac{dx}{2x^2}=\frac{dt}{t+2}$$ This will end up to: $$\int \frac1{2x^2}dx=\int\frac{dt}{t+2}$$
From now on I am not sure how to continue! I ended up having this equation: $$\frac 1 5 x^3 = \ln (t+2)+c$$
I need to find $x(t)$ now. Can somone help please?
update This is how I got $\frac 1{5} x^3$: I said because $\int \frac 1{2x^2}dx$ is $\frac 12 \int x^-2$
isnt it right?