Solving the Equation y'(x) = 1/(x^N+1)

  • Thread starter Thread starter Gregg
  • Start date Start date
  • #31


Hello Gregg and Jackmell

Is that true for the general case? If so, sorry if I said it wasn't.

Yes that's true for the general case. But with + instead of - at denominator, the general term of the series will not be real. On theoretical viewpoint, it doesn't matter : after integration the general term will be a complex logarithm. On the other hand, further simplifications will be laborious.
In order to remain in the real range, it's better to start with a similar series, but with a quadric at denominator. The integation isn't too difficult and leads to a general term including real logarithm and arctangent. (i.e.: attachement)
 

Attachments

  • integral.JPG
    integral.JPG
    26.1 KB · Views: 404

Similar threads

A Volterra equation of the second kind
  • · Replies 1 ·
Replies
1
Views
257
I Understanding Legendre differential equation
  • · Replies 2 ·
Replies
2
Views
5K
I Helmholtz Equation in Cartesian Coordinates
  • · Replies 11 ·
Replies
11
Views
4K
I Solving Differential Equation Using Reduction of Order
  • · Replies 2 ·
Replies
2
Views
3K
A Differential equation and Appell polynomials
  • · Replies 1 ·
Replies
1
Views
3K
A How Do You Construct the Chain Rule for Green's Function in Half-Space?
  • · Replies 1 ·
Replies
1
Views
2K
I Runge-Kutta 4 w/ some sugar on the top: How to do error approximation?
  • · Replies 65 ·
3
Replies
65
Views
7K
I Can I Differentiate Both Sides to Solve y in y^2=ln(1-y^2)?
  • · Replies 2 ·
Replies
2
Views
3K
I Why Lagrange’s method of solving Pp + Qq=R works?
  • · Replies 3 ·
Replies
3
Views
845
I Characteristic curves for ##u_t + (1-2u)u_x = -1/4, u(x,0) = f(x)##
  • · Replies 2 ·
Replies
2
Views
3K