Error function as a solution to a second order ode

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SUMMARY

The discussion focuses on solving the second-order ordinary differential equation (ODE) given by d²y/dx² + 2x(dy/dx) = 0. The solution derived using Maple is y = a*erf(x) + b, where erf(x) represents the error function. The method involves substituting u = dy/dx, transforming the equation into a first-order linear ODE u' + 2xu = 0, which can be solved to find u, followed by integration to obtain y.

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  • Understanding of second-order ordinary differential equations
  • Familiarity with the error function (erf)
  • Proficiency in using Maple for mathematical computations
  • Knowledge of first-order linear differential equations
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  • Study the method of solving first-order linear ODEs
  • Explore the properties and applications of the error function (erf)
  • Learn how to implement differential equations in Maple
  • Investigate the relationship between ODEs and their solutions in mathematical analysis
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Mathematicians, engineering students, and anyone interested in solving ordinary differential equations and applying mathematical software like Maple for complex calculations.

Juggler123
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Hi I need to find the solution of

d^2y/dx^2 + 2x(dy/dx) = 0

I've solved it in Maple and get that

y=a*erf(x)+b

but I have no idea how to arrive at this answer!
Any help would be great, thanks.
 
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Start by letting u=y' then you have:

[tex]u'+2xu=0[/tex]

which I'm sure you know how to solve, then when you get the solution for u, then integrate it once more to get y.
 
Simple! Thanks.
 

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