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4. MW 1-25. Note that y = a would be a solution of (1 - x)y" + zy' -y= (1-z)? if the right side were zero. Use this fact to obtain the general solution of the equation as given. 5. MW 1-26. Consider the differential equation y" + p(x)y' + q(x)y = 0, on the interval a S r S b. Suppose we know two solutions, y1(x) and yz(r), such that V/1 (a) = 0, yz(a) #0, 3/1(b) # 0, 1/2(b) = 0. Give the solution of the equation y" + p(x)y' + q(x)y = f(z), which obeys the conditions y(a) = y(b) = 0, in the form " (x ) = [G(z,1) (2)d2. where G(z, z'), the so-called Green's function, involves only the solutions y, and yz and assumes different functional forms for a' z. Illustrate by solving y" +ky = f(z) , y(a) = y(b) = 0