Problem with differential equation

Click For Summary

Discussion Overview

The discussion revolves around the differential equation (1-x^2)y'' = 2xy' - 2y, focusing on its properties, potential solutions, and methods of approach. The scope includes technical explanations and problem-solving strategies related to ordinary differential equations (ODEs).

Discussion Character

  • Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant questions the clarity of the original question, suggesting that it lacks completeness and cannot be explained as it stands.
  • Another participant proposes that the equation may not have been converted to a homogeneous form, implying that this could be a necessary step for further analysis.
  • A different participant asserts that solving the linear ODE is straightforward, indicating that a first solution is obvious and that the equation can be transformed into a first-order linear ODE.

Areas of Agreement / Disagreement

Participants express differing views on the clarity and solvability of the equation. There is no consensus on the initial question's formulation or the best approach to solving the equation.

Contextual Notes

There are indications of missing assumptions regarding the form of the equation and the methods of solution that may not have been fully articulated by the participants.

jacksonjs20
Messages
9
Reaction score
0
Hi could someone please explain why

(1-x^2)y'' = 2xy'-2y

Many thanks in advance.
 
Last edited:
Physics news on Phys.org
jacksonjs20 said:
Hi could someone please explain why

(1-x^2)y'' = 2xy'-2y

Many thanks in advance.

Your question has no sens. Or the wording is incomplete.
One cannot explain why an equation is an equation.
 
Because you have not converted it to homogeneous like other people would have?
 
Solving the linear ODE : (1-x^2)y'' - 2xy'+2y = 0 is rather easy.
A first solution is obvious. Then the equation can be reduced to a first order linear ODE.
 

Similar threads

Undergrad Why Lagrange’s method of solving Pp + Qq=R works?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Solving Differential Equation Using Reduction of Order
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Why Is a Differential Equation Called Nonlinear?
  • · Replies 3 ·
Replies
3
Views
3K
MHB Second-Order Nonlinear Differential Equation
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Expressing a differential equation into a different format
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad How do I solve this first order second degree differential equation?
  • · Replies 7 ·
Replies
7
Views
4K
Undergrad Integral-form change of variable in differential equation
  • · Replies 1 ·
Replies
1
Views
2K
Insights Differential Equation Systems and Nature
  • · Replies 14 ·
Replies
14
Views
6K
Undergrad Can I Differentiate Both Sides to Solve y in y^2=ln(1-y^2)?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Partial Differential Equation solved using Products
  • · Replies 2 ·
Replies
2
Views
2K