For problems 9-12, determine two linearly independent power series solutions to the given differential equation cen- tered at x = 0. give a lower bound on the radius of conver- gence of the series solutions obtained. 9. (x^2 – 3)y" – 3xy' - 5y = 0. 10. (1 + x^2)y" + 4xy' + 2y = 0. 11. (1 – 4x^2)y" – 20xy' - 16y = 0. 12. (x^2 - 1)y" – 6xy' +12y = 0.

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Ascientist has 50 grams of a radioactive element. the amount of radioactive element remaining after t days can be determined using the equation (1) after two days the scientist receives a second shipment of 50 grams of the same element. the equation used to represent the amount of shipment 2 remaining after t days is 10) - 50 which of the following is an equivalent form of the expression for the amount remaining in shipment 2? what’s the answer?