When asked to prove that x = -1 is a solution to the equation
x2 + 3x + 2 = 0
my lecturer told us that substituting the x = -1 into the equation was not enough as we are assuming we have a solution rather than proving x = -1 was. This confused me.
He went on to show us how to do it which involved subbing in another variable for x say x = x0 and letting the RHS=LHS. To me this was exactly the same as what he had told us not to do which further confused me. So question 1 how can I prove x = -1 is a solution to the above equation.
Also on a tutorial sheet Im working through we have to give examples of ODE's with various properties, namely what order they are, linearity, whether the are homogeneous, autunomous.
in one question Im asked to give example of an ODE of third order, linear, homogeneous and non autonomous..
Is this ok??
d3y/dx3 + d2y/dx2 + dy/dx + xy = 0
the term im not sure of is the xy, would this term effect the linearity of equation? Can an equation be homogeneous and non autonomous??