Question

The problem illustrates the fact that the superposition principle does not generally hold for nonlinear equations. Will post the question so its clear

Answer 1

Show that \[y = \frac{ 1 }{ x } \] is a solution of \[y'+y^2=0\] but that if \[c \neq 1\]and\[c \neq0\] then \[y= \frac{c }{ x }\] is not a solution.
----------------------------------------------------------------------------- What ive done so far is shown that it is a solution of the given DEQ but what I'm getting hung up on is the but if part..?