# Solving Differential Equation (t+2)dx=2x^{2}dt

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

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Linda Birchfield
Note the first: When you divide by $2{x}^{2}$, you have to be careful. Im

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RizerMix
Its

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