Constant Multiples of Solutions. (a) Show that y = e-x is a solution of the l...

Constant Multiples of Solutions.

(a) Show that y = e^-x is a solution of the linear equation

And y = x^-1 is a solution of the nonlinear equation

(b) Show that for any constant C, the function Ce^-x is a solution of equation (16), while Cx^-1 is a solution of equation (17) only when C = 0 or 1.

(c) Show that for any linear equation of the form

if y (x) is a solution, then for any constant C the function Cy(x)is also a solution.