What Does This Equation Mean?
$\Begingroup$ 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...
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$$dx$. Can I use $dx$ alone? Can I simplify above equation by dividing both sides by $dt$? Does $df(x)$ has a meaning alone?
1 Answer
Hint: This is a first-order nonlinear ordinary differential equation, let
$$y = v t \rightarrow y' = v + v' t$$
This is also Bernoulli's equation.
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