Williamson's synthesis involves an SN2 reaction mechanism and is widely used for asymmetric ether synthesis.
Step 1: Williamson's synthesis is used for the preparation of ethers.
Step 2: Reaction: \[ R-O^- + R'-X \rightarrow R-O-R' + X^- \] where \( R'X \) is an alkyl halide and \( R-O^- \) is an alkoxide ion.
Step 3: Example: \[ C_2H_5ONa + CH_3I \rightarrow C_2H_5OCH_3 + NaI \]
(b) Order of the differential equation: $ 5x^3 \frac{d^3y}{dx^3} - 3\left(\frac{dy}{dx}\right)^2 + \left(\frac{d^2y}{dx^2}\right)^4 + y = 0 $