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.Step 2Method of Solving linear equationFirst we have to write the equation in standard form Compare the standard form with the giving equation So, we have Now, we have to calculate the integrating factor Then, Now, we have to multiply the standard equation with or = Hence, we can say that is a solution of the homogenous equationStep 3Method of Solving linear equationFirst we have to write the equation in standard form Compare the standard form with the giving equation...