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Solve: x^2 y'' + 5xy' + 13y = 0

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Solve: x2 y'' + 5xy' + 13y = 0

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Best answer

The characteristic equation is 

m ( m - 1 ) + 5 m + 13 = 0 

or m = – 2 + 3 i and - 2 - 3 i 

Thus, the general solution is 

y = x–2 [ c1 cos (3ln|x|) + c2 sin (3ln|x|) ]

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