Step 1: The Hardy-Weinberg principle is a fundamental concept in population genetics, stating that allele frequencies in a population will remain constant from generation to generation in the absence of evolutionary influences.
Step 2: For the Hardy-Weinberg equilibrium to hold, the following conditions must be met: 1. Large population size. 2. Random mating. 3. No mutation. 4. No migration. 5. No natural selection.
Step 3: The principle is mathematically expressed as: \[ p^2 + 2pq + q^2 = 1 \] where \(p\) is the frequency of the dominant allele and \(q\) is the frequency of the recessive allele.
(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 $