Question

Are the given equations suitable for the Method of Undetermined Coefficients? Answer "YES" or "NO":

a) y'' - 6y' + 8y = t^1/3 +1

b) 2y'' - y' - y = (t^3 - 2t^2 + 3)sin(t/4)

Answer 1

a) Answer: No

Explanition: The given differential equation is y" -6y'+8y= t^1/3 +1

is not suitable for the method of undetermined coefficients .

Since RHS is  t^1/3 +1 is not in the form At^m+B, where m= 0, 1,2,,,

b) Answer: YES

Explanition: The given differential equation is 2y" -y'- y= (t^3 -2t^2+3) sin(t/4)

is suitable for the method of undetermined coefficients .

Since RHS is  (t^3 -2t^2+3) sin(t/4) is of the form (At^3+Bt^2 +ct +D) sin (pt),