What is the Solution to the 2nd Order Nonlinear ODE y'' = x^2 * y?

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SUMMARY

The discussion focuses on solving the second-order nonlinear ordinary differential equation (ODE) given by y'' = x^2 * y. The equation is identified as a special case of the Emden-Fowler equation. Users express the need for a solution, with one participant mentioning the lack of access to Mathematica and referring to external resources like Wolfram Alpha for potential solutions.

PREREQUISITES
  • Understanding of second-order ordinary differential equations
  • Familiarity with nonlinear dynamics
  • Knowledge of the Emden-Fowler equation
  • Basic proficiency in using computational tools like Wolfram Alpha
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  • Research the Emden-Fowler equation and its applications
  • Explore numerical methods for solving nonlinear ODEs
  • Learn how to use Mathematica for differential equations
  • Investigate alternative computational tools for solving ODEs
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Mathematicians, physicists, and engineers dealing with nonlinear differential equations, as well as students seeking to deepen their understanding of ODE solutions.

mistergrinch
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I'm trying to solve the equation y'' = x^2 * y. This looks like it should be simple, but I don't have mathematica and the only reference I've found calls it a special case of the Emden-Fowler equation and refers to a solution in a book I don't own. Does anyone know the solution to this equation? Thanks.
 
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http://www.wolframalpha.com/input/?i=y%27%27%3Dx^2+y&x=0&y=0

:)
 

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