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Trial and error method of solving a 4th degree differential equation > For the 4 th degree DE it is of form v(4) + 2y(-)+ y=4 cos (x) + 8 xsin(x) try first with 1 st choice = Y= A.x cos(x) + Box . sin(x) 2 nd choice = Y= A.cos(x) + B.x 'sin(x) so in class we show that the above two choices will lead to dead end. > verify that this choice of solution works, third choice = Y= A.x cos(x) + B.x' sin(x) > Y:= Ax cos(x) + B.x sin(x) Y:= Ax cos(x) + Bx' sin(x) (1.1) > 2 A cos(x) - 4 Ax sin(x) - Ax cos(x) + 6 Bx sin(x) + 6 Bx cos(x) - Bx' sin(x) (1.2) [> we calculated the 2 nd derivative as above , continue with the 3 rd and 4 th derivative and set up the equation to solve for A and B