Question 1184638


a)  {{{W(y[1],y[2],y[3]) = abs(matrix(3,3, sinh(3x), cosh(3x), e^(3x), 3cosh(3x), 3sinh(3x), 3e^(3x), 9sinh(3x), 9cosh(3x), 9e^(3x))) = 


27e^(3x)abs(matrix(3,3, sinh(3x), cosh(3x), 1, cosh(3x), sinh(3x), 1, sinh(3x), cosh(3x), 1)) = 0}}}.

***This is expected since the set { {{{y[1]}}}, {{{y[2]}}}, {{{ y[3]}}}} is linearly dependent, because {{{y[1] + y[2] = sinh(3x) + cosh(3x) = e^(3x)=y[3]}}}.


b)  No, { {{{y[1]}}}, {{{y[2]}}}, {{{ y[3]}}}} is not a fundamental set for the D.E. (i.e., it cannot be a basis for the solutions of the D.E.).