$\begingroup$

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?

$\endgroup$ 1

1 Answer

$\begingroup$

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.

$\endgroup$ 1

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy