Thread: Can someone help with and explain this differential equation?

I know it looks easy, but my working does not look right!

(x² + 1) dy/dx - 2xy = 2x (x² + 1)

1) which analytical method would you use to solve this equation?
and therefore solve expressing y explicitly as a function of x.
Hence find the particular solution of the differential equation that satisfies the initial condition y(0) = 1

Many thanks

Hi. I would divide through by . That puts it into standard form of a first order ode. Now calculate the integrating factor and proceed.

I am working on this similar problem - I think I have got to the last step and am trying to integrate the following...



Should be integrating this by parts?

I have seen in another text where this has been integrated it in one go but I don't know if this is right?

Please help!!

You can integrate this by substitution, let:



Then



And then:



Which turns your integral into:



Or you can recognize that:



Your integral would be:



Which is really easy as well.