Consider the differential equation x2y” − 8xy’ + 18y = 0; x3, x6, (0, [infinity]). Verify that the given functions form a fundamental set o

Question

Consider the differential equation x2y” − 8xy’ + 18y = 0; x3, x6, (0, [infinity]). Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. The functions satisfy the differential equation and are linearly independent since W(x3, x6) = Incorrect: Your answer is incorrect. ≠ 0 for 0 < x < [infinity].

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Liliana 2 weeks 2022-01-01T17:20:00+00:00 1 Answer 0 views 0

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    2022-01-01T17:21:14+00:00

    Answer: The equation is differentiated implcitly, with respect to x and y

    Step-by-step explanation: x2y – 8xy + 18y = 0

    By implicit differentiation: 2y + 2xdy/dx – (8y + 8dy/dx) – 18dy/dx = 0

    2y – 8y – 8dy/dx – 18dy/dx +  2xdy/dx = 0

    -6y + 2xdy/dx – 26dy/dx = 0

    2xdy/dx – 26dy/dx = 6y

    dy/dx(2x – 26) = 6y

    ∴ dy/dx = 6y/2(x – 13) = 3y/(x – 13)

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