Hi all,

I am given that y1 = x, y2 = cos(log(x)) and y3 = sin(log(x)) are all solutions to the DE y'''+(2/x)y''+(1/x^2)y'-(1/x^3)y=0 for x>0, I have already calculated the 1st and 2nd derivatives of the solutions and put then into a matrix to find the Wronskian determinant. How to I find the determinant and then find out whether or not its equal to zero to tell if the solutions are linearly independent. I tried and failed, as it just became a whole big mess of sine’s and cosine’s. Could anyone help me find the Wronskian determinant?

Thanks.