Is this initial-value problem separable? I have \(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\frac{{{2}{\left({x}^{{3}}+{x}^{{2}}-{x}+{1}\right)}{y}}}{{{x}^{{4}}-{1}}}},;{y}{\left({0}\right)}={1}.\) I

Cash Duncan

Cash Duncan

Answered question

2022-04-15

Is this initial-value problem separable?
I have dydx=2(x3+x2x+1)yx41,;y(0)=1.
I tried separating it and got 2y1dy=(x3+x2x+1)(x41)1
I am unsure if that separation is correct, would anyone be able to clarify?

Answer & Explanation

posciad48o

posciad48o

Beginner2022-04-16Added 15 answers

It would be correct if the right hand side of your equation included dx, and you wrote (2y)1:
,dy2y=x3+x2x+1x41dx=x3+x2x+1(x2+1)(x+1)(x1),dx.
The left hand side is relatively easy to integrate; you can use partial fraction decomposition on the right-hand side. Can you take it from here?

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?