The Amazon River is an important river in South America. It is the longest river by discharge of water in the world and plays a critical role in the ecosystem of the Amazon Rainforest. The river is central to transportation, trade, and agriculture in the region. It also supports a vast array of biodiversity and influences global climate patterns
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 $