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If y=Acos(logx)+\ Bsin(logx) , prove tha...

If `y=Acos(logx)+\ Bsin(logx)` , prove that `x^2\ (d^2y)/(dx^2)+x(dy)/(dx)+y=0` .

Text Solution

Verified by Experts

We have given
`y=Acos(logx)+\ Bsin(logx)`
Then we have to proof
`x^2\ (d^2y)/(dx^2)+x(dy)/(dx)+y=0`
As,
`y=Acos(logx)+\ Bsin(logx)`
On differentiating w.r.t. x, we get
`(dy)/(dx)=a([-sin(log x)])/(x)-(bcos(log x))/(x)`
...
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Knowledge Check

  • If y=acos(log x)-bsin(log x), then the value of x^2(d^2y)/(dx^2)+xdy/dx+y is

    A
    4
    B
    0
    C
    2
    D
    3

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