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If y=xlog"{"x/((a+b x))"]" , then show t...

If `y=xlog"{"x/((a+b x))"]"` , then show that `x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2dot`

A

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

B

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

C

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

D

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

Text Solution

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To solve the problem, we need to show that: \[ x^3 \frac{d^2y}{dx^2} = \left( x \frac{dy}{dx} - y \right)^2 \] Given: ...
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CENGAGE ENGLISH-DIFFERENTIATION-Execrises
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  8. Let f(x) be a polynomial of degree 3 such that f(3)=1,f^(prime)(3)=-1,...

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  9. If y^2=a x^2+b x+c , then y^3(d^2y)/(dx^2) is (a) a constant (b) a fun...

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  11. if y= sin mx, them the value of the determinant |{:(y,,y(1),,y(...

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  13. Let y=1n(1+cosx)^2 . Then the value of (d^2y)/(dx^2)+2/(e^(y/2)) equal...

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  18. "If "x=phi(t), y=psi(t)," then "(d^(2)y)/(dx^(2)) is

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