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I have an exam tomorrow and I was trying to solve my Homework questions. I am stuck at this question:

Find the general solution of the equation $$tdy + ydt = 3t^3y^2dt$$

It was exactly written as above. I am confused.

I can get $df(x)/dx$, take the derivative of $f(x)$ one time acording to $x$ or when you write $dx$ with an $\int$ sign as $\int$$dx$. Can I use $dx$ alone? Can I simplify above equation by dividing both sides by $dt$? Does $df(x)$ has a meaning alone?

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    $\begingroup$ This equation is separable. $\endgroup$
    – user61527
    Commented Dec 17, 2013 at 2:13

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Hint: This is a first-order nonlinear ordinary differential equation, let

$$y = v t \rightarrow y' = v + v' t$$

This is also Bernoulli's equation.

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  • $\begingroup$ Short and sweet it is! +1 $\endgroup$
    – amWhy
    Commented Dec 18, 2013 at 0:05

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