How can I solve this non-linear second order differential equation?

Thread starter peterisxxx
Start date May 5, 2011
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Non-linear

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The discussion focuses on solving the non-linear second-order differential equation given by u'' + u'/x + C = 0, where u is a function of x and C is a constant. A participant suggests multiplying the equation by x², transforming it into x²u'' + xu' + cx² = 0, which resembles an Euler-Cauchy differential equation. The solution involves addressing the homogeneous part and subsequently finding a particular integral for cx².

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May 5, 2011

peterisxxx

u''+u'/x+C=0
u-function of x, C - const

could someone solve it for me or at least give a hint??

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May 5, 2011

rock.freak667

Homework Helper

if you multiply throughout by x^2 you will get

x^2u'' + xu' + cx^2 = 0

which the first part looks like a Euler-cauchy DE so you can solve the homogenous part and then solve for the PI of cx^2.