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If (a+bx)e^(y/x)=x , Prove that x^3(d^2y...

If `(a+bx)e^(y/x)=x` , Prove that `x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2`

A

`((dy)/(dx)+x)^(2)`

B

`(x(dy)/(dx)-y)^(2)`

C

`((dy)/(dx)-y)^(2)`

D

`(x(dy)/(dx)+y)^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`(y)/(x)=logx-log(a+bx)`
`therefore" "(x(dy)/(dx)-y)/(x^(2))=(1)/(x)-(b)/(b+ax)=(a)/(x(a+bx))`
`therefore" "x(dy)/(dx)-y=(ax)/(a+bx)" (1)"`
Differentiating again, we get
`x(d^(2)y)/(dx^(2))=(a^(2))/((a+bx)^(2))`
`therefore" "x^(3)(d^(2)y)/(dx^(2))=(a^(2)x^(2))/(a+bx)^(2))=((xdy)/(dx)-y)^(2)`
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