Question: Answer this question ASAP Recall that there are two apparently different versions of the Wronskian: A. The Wronskian of two solutions y1 (t) and y2

Answer this question ASAP

Answer this question ASAP Recall that there are two apparently different versions

Recall that there are two apparently different versions of the Wronskian: A. The Wronskian of two solutions y1 (t) and y2 (t) to the second-order linear equation y" + p(t)y' + q(t)y = 0 is defined to be the 2 x 2 yi (t) yz(t) determinant y'(t ) yz (t ) B. The Wronskian of two vector solutions x(1) (t) and x(2) (t) to the two- variable first-order system of linear equations x' (t) = Ax(t) for the 2 x 2 matrix A is defined to be the 2 x 2 determinant | x(1) x(2) |. (Here x(1) (t) and x(2) (t) form the two columns in the determinant.) Further recall that the second-order linear equation can be converted into a two-variable linear system by defining x," (t) = y1(t) and x2 ) ( t ) = yi (t), so x(1) (t) = y1 (t ) Lyi(t ) and similarly for x(2) (t). Prove: the two apparently different notions of the Wronskian are constant multiples of each other, in this case

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