Power series solution
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Compute the power series solution for the ODE y''+x^2y=0 and determine the radii of convergence for the two series solutions.
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This provides an example of power series solution and radii of convergence.
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------------------------------(i)
Comparing the equation with the equation
, we get
does not vanish at .
Then is an ordinary point.
Let the solution in series form be
---------------(ii)
------------(iii)
Putting the values of in (i), we get
or,
This is an identity. Equating the coefficients of various powers of to zero, we get the following relations:
------------------(iv)
------------------(v)
----------------(vi)
...
Education
- BSc, Manipur University
- MSc, Kanpur University
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