I have this question as an assignment, puzzled with one bit...
let y = Q(x) be any solution to the differential equation.
dy/dx = xy
Answer each of the following without solving this DE.
(i) In terms of x only, what is the slope of Q as it crosses the line y = x ?
(ii) What is the slope of the line y = x ?
(iii) " In the region x > 1, the graph of Q can only cross the line y = x from below" Is this statement true or false??
(i)= slope = dy/dx = xy = x . x = x2
(iii)= TRUE = but the only way i found it to be true is by solving the DE and graphing it which is not allowed by the question. Am i right firstly in saying it is true and if so how would I know this without solving DE??