Find all values of m so that the function $y = x^m$ is a solution of the given differential equation. (Enter your answers as a comma-separated list.) $x^2y'' - 10xy' + 30y = 0$ m =
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Now, let's substitute y and y' into the given differential equation: 2y - 10xy' + 30y = 0 2(x^m) - 10x(mx^(m-1)) + 30(x^m) = 0 Simplifying this equation, we get: 2x^m - 10mx^m + 30x^m = 0 (2 - 10m + 30)x^m = 0 For this equation to hold true for all x, the Show more…
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