Example 1: If u(x, y) = x³y² + x² - 3y + 4 find a²u e) a²u a2u a2u ди and f) дудх ди а) Əx b) c) ду d) дхду ду?

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A: Ans are provided below for 1 question in homework

Dimensional homogeneity

The term dimensional homogeneity means that in an equation, the dimensions of each term on both sides are equal, which means the dimensions of the left-hand side (LHS) of an equation are similar to the dimensions of the right-hand side (RHS). For a dimensionally homogeneous equation, the powers of fundamental dimensions will be identical on both sides of the equation.