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

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 the solution using sigma notation with a formula for the coefficients. Write the two linearly independent solutions that form the general solution.

b) Find a power series solution satisfying the initial conditions y(0) = 2 and y' (0) = 3. Write the first six nonzero terms of the solution. And write the solution using sigma notation with a formula for the coefficients.

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Expert Solution

Colby Messinger answered 1 year ago
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