What is Tollen's reagent? Write the chemical equation of the reaction of aldehyde with Tollen's reagent.
Tollen's test is used to distinguish aldehydes from ketones as only aldehydes undergo oxidation.
Step 1: Definition:
Tollen's reagent is an ammoniacal silver nitrate solution that oxidizes aldehydes to carboxylates, forming a silver mirror.
Step 2: Reaction: \[ R-CHO + 2[Ag(NH_3)_2]^+ + 3OH^- \rightarrow R-COO^- + 2Ag + 4NH_3 + H_2O \]
Find the values of \( x, y, z \) if the matrix \( A \) satisfies the equation \( A^T A = I \), where
\[ A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix} \]
(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 $