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?