Opium is a dried latex obtained from the seed capsules of the opium poppy plant Papaver somniferum .Opium is a narcotic substance extracted from the latex of the opium poppy plant. It contains alkaloids like morphine and codeine, which are used for medicinal and recreational purposes.
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 $