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Find a solution in the form of a power series for an ODE

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Find a solution in the form of a power series for the equation

y" - 2*x*y' = 0

(ie find 2 linearly independent solutions y1(x) and y2(x)).

After doing that, note that the equation can also be solved directly by integration:

y"/y' = 2x
ln(y') = x^2 + c1
y' = ke^(x^2) k=e^c1

y = k* integral((e^(t^2))dt + C) from 0 to x

Thus, one of your power series solutions gives and explicit form for the integral:

integral(e^(t^2)dt) from 0 to x

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A solution is found in the form of a power series for an ODE.

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