Consider a second order nonhomogeneous, near differential equation of the form w

Question

Consider a second order nonhomogeneous, near differential equation of the form where y s the dependent function which is a function of the independent variable ao, al, and a2 are constant coefficients; and g(z) s called the input function. Using the Method of undetermined coefficients requires a guess for the particular solution yp (a) based on the form of the input function. Match each guess for the particular solution yp (z), with its appropriate input function g(z) A. Does not match any of the options yp (a) (Az B) cos (3a) (Car D) sin (3z) yp (z) Ae" cos (2z) Be sin(2z) yp(z) A, cos(3a) B cos(2a) sin D sin(2a) yp (z) Acos(3a) B sin(3z)

Explanation / Answer

1 ---> D

For cos2x + sin3x,

we need Acos2x +Bsin2x + Ccos3x + Dsin3x, which is option D

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2 ---> B

3 ---> E

4 ---> C

5 ---> A

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