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If x=sin(1/alogy),"s h o wt h a t"(1-x^...

If `x=sin(1/alogy),"s h o wt h a t"(1-x^2)y_2-xy_1-a^2y=0.`

Text Solution

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Here,

`x=sin (frac{1}{a} log y) `

`Rightarrow frac{1}{a} log y=sin ^{-1} x`

`Rightarrow y=e^{a sin ^{-1} x}`

Differentiating w.r.t `x`, we get

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Knowledge Check

  • If y=(sin^(-1)x)^(2)," then "(1-x^(2))y_(2)-xy_(1)=

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    `m^(2)y`

  • If y=1/2(sin^(-1)x) , then (1-x^2)y_2-xy_2=?

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    `-1`
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