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padilas [110]
3 years ago
11

Find all values of m so that the function y = xm is a solution of the given differential equation. (Enter your answers as a comm

a-separated list.)
x^2y'' − 14xy' + 54y = 0

m =
Mathematics
1 answer:
blagie [28]3 years ago
8 0

Answer:

m = 6,9  

Step-by-step explanation:

We are given that y = x^m is a solution to given differential equation.

x^2y'' - 14xy' + 54y = 0  

First we 3evaluate the value of:

y'' = m(m-1)x^{(m-2)}

y' = mx^{(m-1)}

Putting these value in the above differential equation, we get,

x^2m(m-1)x^{(m-2)} + 14xmx^{(m-1)} + 54x^m = 0

x^m[m(m-1) -14m + 54] = 0

x^m(m^2 - 15m + 54) = 0

(m^2 - 15m + 54) = 0

(m-9)(m-6) = 0

m = 9,6

Thus, for m = 9,6 , the function y = x^m is a solution of given differential equation.

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