(a) Verify that if c is a constant, then the following piecewise-defined function satisfies the differential equation y' = 2vy for all x (including the point x = c). Construct a figure illustrating the fact that the initial value problem y' = 2vy, y(0) =0 has infinitely many solutions. 0 for x = c y ( x ) = ( x - c ) 2 for x > c (b) For what values of b does the initial value problem y' = 2 vy , y(0) = b have (i) no solution, (ii) a unique solution that is defined for all x? (a) Find the derivative of y(x). 0 for x = C y' ( x ) = 1 2 ( x - c) for x > c Substitute the values of y' and y for x s c into the given differential equation. y' = 2vy 0 = 210 Does y satisfy the given differential equation for x s c? Yes O NoSubstitute the values of y' and y for x > c into the given differential equation. y' = 2vy 2 ( X - C ) = 21 ( x - c ) 2 Does y satisfy the given differential equation for x > c? O No Yes Construct a figure illustrating the fact that the initial value problem y' = 2vy, y(0) =0 has infinitely many solutions. Choose the correct graph below. O A. O B. (0,0) (0,0)O C. CD. (0,0) 1/111311 (0,0) (b) (i) The initial value problem y' = 2vy , y(0) = b has no solution for b 0 (Simplify your answer.)