Solving a Non-Linear ODE: What Method Should I Use?

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Homework Help Overview

The discussion revolves around solving the non-linear ordinary differential equation (ODE) y' = x^2 + y^2 with the initial condition y(0) = 1. Participants are exploring methods to approach this first-order ODE.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts various methods including separable variables, exact equations, and considerations of linearity, but finds them ineffective. Some participants mention the equation's classification as a Riccati equation and suggest transformations to simplify it. Others express uncertainty about how to identify a particular solution.

Discussion Status

The discussion is ongoing, with participants exploring different methods and questioning the assumptions behind the problem. There is no explicit consensus, but suggestions for transformations and the need for a known solution are noted as points of interest.

Contextual Notes

Participants highlight the challenge of finding solutions without an initial known solution, which is a key constraint in addressing the problem.

lkh1986
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Homework Statement



Solve y'=x^2+y^2 with initial condition y(0)=1.


Homework Equations


This is a first order ODE.



The Attempt at a Solution


I have tried separable variable, exact, and homogeneous and non-homogeneous, but none of them work. It's neither linear nor Bernoulli.

Any clue on what method have I missed or should I tried? Thanks.
 
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It is a http://en.wikipedia.org/wiki/Riccati_equation" .
 
Last edited by a moderator:
Metaleer said:
It is a http://en.wikipedia.org/wiki/Riccati_equation" .

Thanks. I will try using some suitable transformation to reduce it to a solvable linear DE. :)
 
Last edited by a moderator:

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