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(5 points) An equation in the form y' + p(x)y = q(x)y" with n 9L- 0, 1 is called a Bernoulli equation and it can be solved using the substitution 0 = y\"" which transforms the Bernoulli equation into the following first order linear equation for u: u' + (1 n)p(x)v = (1 n)q(x) Given the Bernoulli equation 9 4 2 y'+;y=48x y3 (*) we have n = so 0 = We obtain the equation 0" + v = Solving the resulting first order linear equation for v we obtain the general solution (with arbitrary constant C) given by u = Then transforming back into the variables x and y and using the initial condition y(1) = 1 to nd C = Finally we obtain the explicit solution of the initial value problem as y: (3 points) It can be shown that yl = e" and y2 = ace2x are solutions to the differential equation y\" + 43/ + 4y = 0 on the interval (00, 00). Find the Wronskian of 3/1 , y2 (Note the order matters) W91! 3'2) = Do the functions yl , yz form a fundamental set on (00, co)? Answer should be yes or no