Wronskian. For any two differentiable functions y1 and y2 , the function (18) is ca...

Wronskian. For any two differentiable functions y1 and y2 , the function (18) is called the Wronskian of y1 and y2. This function plays a crucial role in proof of Theorem 2. (a) Show that W[y1,y2] can be conveniently expressed as the determinant (b) Let y1(t),y2(t) be a pair of solutions to the homogeneous Equation (with ) on an open interval I. Prove that y1(t) and y2(t) are linearly independent on I if and only if their Wronskian is never zero on I. [Hint: This is just a reformulation of Lemma 1.] (c) Show that if y1(t) and y2(t) are any two differentiable functions that are linearly dependent on I, then their Wronskian is identically zero on I.