# What does this equation mean?

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$$dx. Can I use dx alone? Can I simplify above equation by dividing both sides by dt? Does df(x) has a meaning alone? - This equation is separable. – user61527 Dec 17 '13 at 2:13 ## 1 Answer Hint: This is a first-order nonlinear ordinary differential equation, let$$y = v t \rightarrow y' = v + v' t$\$

This is also Bernoulli's equation.

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Short and sweet it is! +1 – amWhy Dec 18 '13 at 0:05