Assuming an equation without variables is true. Can I by logical steps get to an unanimous ever true or false statement and then decide if the original equation is true?

Answer 1

Yes are you familiar with Differential Equations? I think you are specifically looking for the term " Initial Value " theory.

Answer 2

An equation without variables is either true or not true. No assuming is needed

e.g.,

4 = 4, true

4 = 5, false