Let `y=f(x) and x=(1)/(z)." If "(d^(2)y)/(dx^(2))=lamda_(z^(3))(dy)/(dz)+z^(4)(d^(2)y)/(dz^(2))`, then the value of `lamda` is

Options

A. 1
B. 2
C. `(1)/(2)`
D. `(1)/(4)`

Explanation

To solve the problem, we need to find the value of \( \lambda \) in the equation:

\[ \frac{d^2y}{dx^2} = \lambda z^3 \frac{dy}{dz} + z^4 \frac{d^2y}{dz^2} \]

Given that \( y = f(x) \) and \( x = \frac{1}{z} \), we will differentiate \( y \) with respect to \( x \) and \( z \) step by step.

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