Can Euler's Method Solve dy/dx = x + y^2?

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Homework Help Overview

The discussion revolves around the differential equation dy/dx = x + y^2. Participants are exploring the nature of the equation and the methods for solving it, including the potential use of Euler's method.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the difficulty of separating variables and integrating the equation. Some question whether the original equation was derived from another problem, while others suggest alternative forms that may be easier to solve.

Discussion Status

The conversation includes various interpretations of the equation and its solvability. Some participants have offered insights into the complexity of the solution, noting that it may not be elementary, while others mention the applicability of Euler's method without reaching a consensus on the best approach.

Contextual Notes

There is uncertainty regarding the original problem context and whether the equation was derived from a different exercise. Participants are also considering the implications of the equation's form on its solvability.

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Easy differential equation??

I appreciate any help with this problem.

dy/dx =x+y^2

I need to solve it but i tried to do this by seperating the variables and i can 't do it. And then i need to integrate that to find y.


Thanks for help
 
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This doesn't look like an easy differential equation to me. Is solving the differential equation the exercise or did you find that differential equation by trying so solve another problem?
 


The solution isn't elementary (Mathematica gives a messy solution which uses the Bessel function).
 


Are you sure you don't mean [tex]\frac{{dy}}{{dx}} = xy^2[/tex]? That's a separable equation
 


Hello, thanks for helping. It turned out it can be solved using Euler's method,
 

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