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.

SolutionStep 1In this problem, we have to show that is a solution of the homogenous equation And is a solution of the nonlinear equation. b)In the next part, we have to show that for any constant C, the function Ce-x is a solution of equation , while Cx-1 is a solution of equation only when C = 0 or 1.c)In this problem we have to show that for any linear equation of the form if (x) is a solution, then for any constant C the function C(x)is also a solution.