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(Solved): Find two power series solutions of the given differential equation about the ordinary point x=0 ...


Find two power series solutions of the given differential equation about the ordinary point \( x=0 \). \[ \begin{array}{l} y^

Find two power series solutions of the given differential equation about the ordinary point .


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To find power series solutions of the given differential equation about the ordinary point x=0, we can assume a power series solution of the form:
   to infinity  

We can differentiate this series twice to obtain:

  to infinity  

Now, we substitute y and   in the differential equation and obtain:
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