What is the solution of the follwoing differential equation

where is a constant.

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- December 22nd 2012, 09:00 AMJulieKNonlinear second order differential equation
What is the solution of the follwoing differential equation

where is a constant. - December 22nd 2012, 09:41 AMjakncokeRe: Nonlinear second order differential equation
Ok, This method works for all equations of the form .

Now Assume a new variable, v = y'. So

Since This now becomes

Now you have a Differential equation of the first order, . For your specific equations turns into a seperable ODE,

which turns into

So v =

Now again Since which means

and you get some super ugly integral. - December 22nd 2012, 12:00 PMJulieKRe: Nonlinear second order differential equation
Thank you

- December 23rd 2012, 01:06 AMJJacquelinRe: Nonlinear second order differential equation
Hi !

The obvious solutions are y(x)=constant.

The other solutions cannot be expressed as a combination of a finit number of elementary functions.

They involves some special functions such as li(x) or Ei(x) :

Logarithmic Integral -- from Wolfram MathWorld

Exponential Integral -- from Wolfram MathWorld

About special functions, pp.18-36 of the paper "Safari on the contry of special Functions" :

JJacquelin's Documents | Scribd - December 26th 2012, 01:47 AMtomjacksonRe: Nonlinear second order differential equation
Can someone please confirm that the above solution is OK? I tried a lot but I could not find the result. Is there any other way to solve this problem? I could not find any divisor for R[x].

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