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Verify that the function y = 2lambda x +...

Verify that the function `y = 2lambda x + (mu)/(x)` where `lambda, mu` are arbitary constants is a solution of the differential equation `x^(2)y'' + xy' - y = 0`.

Text Solution

Verified by Experts

`y' = lambda - (mu)/(x^(2))` & `y'' = (2mu)/(x^(3))`
Substituting y' and y'' in the R.H.S. of the given differential equation we get
`R.H.S. = x^(2) ((2 mu)/(x^(3))) + x (lambda - (mu)/(x^(2))) + (lambda x + (mu)/(2))`
`= (2mu)/(x) + lambda x - (mu)/(x) - lambda x - (mu)/(x)`
= 0
= L.H.S.
`:.` The given function is a solution of the given differential equation.
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