A question on undetermined coefficients

[shemer77]

Homework Statement

http://gyazo.com/6c440aa92106f729639c91f6d59dcd89

The Attempt at a Solution

My question is why is yp = At^3+Bt^2 +Ct. The reason I ask that is because is see t^2+2t so why wouldn't it be yp=At^2 +Bt +c?

 

[SammyS]

Homework Statement

http://gyazo.com/6c440aa92106f729639c91f6d59dcd89

The Attempt at a Solution

My question is why is yp = At^3+Bt^2 +Ct. The reason I ask that is because is see t^2+2t so why wouldn't it be yp=At^2 +Bt +c?

Because (D³ + 4D)( At³+Bt² +Ct) = 12At² + 8Bt + 6A + 4C .

Whereas, (D³ + 4D)( At²+Bt+C) = 8At + 4B, which is not a quadratic.

.