Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
This equation is separable. – user61527 Dec 17 '13 at 2:13
up vote 3 down vote accepted

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.

share|cite|improve this answer
Short and sweet it is! +1 – amWhy Dec 18 '13 at 0:05

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.