Find the annihilator for each function and use the method of undetermined coefficients to find a particular solution to each of the equations: If y'''+4y'-5y= 12x^3-7x. The annihiltor for any polynomial is the derivative to the degree +1 so D^4 in this case. But my question is based on the undetermined coefficients portion, the Homogeneous solution should be in the form Y(h)= C1e^(x) + C2e^((-1/2)x)Cos((squareroot(19)/2)x)+C3e^((-1/2)x)Sin((squareroot(19)/2)x). You don't replace the Constants of the homogeneous with equations of x and then plug back in the original equation do you?

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