Question

While solving a partial differential equation using a variable separable method, we assume that the function can be written as the product of two functions which depend on one variable only.

(a) True

(b) False

The question was posed to me in a national level competition.

Query is from Solution of PDE by Variable Separation Method topic in portion Applications of Partial Differential Equations of Engineering Mathematics

Answer 1

Right option is (a) True

Explanation: If we have a function u(x,t), then the function u depends on both x and t. For using the variable separable method we assume that it can be written as u(x,t) = X(x).T(t) where X depends only on x and T depends only on t.