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Diff. equations Consider the equation (x^2 ? 2)y''+ 3xy'+ y = 0. a) Find the general solution...

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Advance Math

Diff. equations

Consider the equation (x^2 ? 2)y''+ 3xy'+ y = 0.

a) Find the general solution as a power series centered at x =0. Write the first six nonzero terms of the solution. And write thesolution using sigma notation with a formula for the coefficients.Write the two linearly independent solutions that form the generalsolution.

b) Find a power series solution satisfying the initialconditions y(0) = 2 and y' (0) = 3. Write the first six nonzeroterms of the solution. And write the solution using sigma notationwith a formula for the coefficients.

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