What is the solution of the follwoing differential equation
where is a constant.
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.
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" :
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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].