How do I go about solving this PDE?

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Homework Help Overview

The problem involves a differential equation presented in the form of a second-order equation, initially framed as a partial differential equation (PDE) but later referred to as an ordinary differential equation (ODE). The equation includes a nonlinear term dependent on the variable X.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants explore whether X represents a vector or a single variable, which influences the classification of the equation. Some suggest rewriting the equation in polar coordinates or applying separation of variables. Others inquire about the method of separation of variables and express confusion regarding the nature of the equation.

Discussion Status

The discussion is ongoing, with participants questioning the classification of the equation and exploring different methods for solving it. There is no explicit consensus on the approach, but various lines of reasoning are being examined.

Contextual Notes

There is uncertainty regarding whether the equation should be treated as a PDE or an ODE, which affects the proposed methods of solution. Participants are also navigating the implications of the nonlinear term in the equation.

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Homework Statement



\frac{\partial^2X}{\partial a^2} + (X^4-1)\frac{\partial X}{\partial a} = 0


Homework Equations



How do I go about solving this PDE ?

The Attempt at a Solution



Please help !
 
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Is X a vector? Then I would try rewriting it in polar coordinates. Otherwise this isn't a PDE and could be solved with the same method as is used with separation of variables.
 


How do you solve with s.o.v. ?
 


coverband said:
How do you solve with s.o.v. ?
Is it a pde or not? Ie, is X a vector or a single variable? As for how to solve it if it is an ODE, just integrate it with respect to a and then solve normally.
 


Ok. Let's call it an ODE: \frac{d^2y}{dx^2} + (y^4-1)\frac{dy}{dx} = 0

Now how solve please !
 

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