Question: Please explain step-by-step solutions for questions 7 and 8. Please Clear handwriting 7') 3) a} Show that the functions 9.1 , cos 2x, and sin

Please explain step-by-step solutions for questions 7 and 8.

Please Clear handwriting

7') 3) a} Show that the functions 9.1 , cos 2x, and sin 23: are linearly independent. In) Find a homogeneous differential equation with the above functions as a basis. Let y" + cry\" + by = 11x). Suppose the homogeneous solution is yh = C13\" + Cze a) What are the values of a and b'? b) Suppose T06) = 4x2 + 3 cos x, what will be your choice of yp'? e) Suppose T06) = 433' + 33:, what will bc your choice of yp'? d) Suppose r06) = 9'\" cos 4 36, what will be your choice of yp'? 3x

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