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## Homework Statement

Solve:

[tex]\frac{d^2y}{dx^2}+\frac{dy}{dx}=3x^2+2x+1[/tex]

## The Attempt at a Solution

Well the C.F. is [itex]y=C_1e^{-x}[/itex]

the P.I. is of the form [itex]y_{PI}=Ax^3+Bx^2+Cx+D[/itex]

I can find the values of A,B and C bu differentiating it and substituting it into the equation. But How would I find D since there is no 'y' in the ODE given and differentiating [itex]y_{PI}[/itex] makes the constant disappear.

(Note: I can find the answer by integrating it w.r.t x and then using the integrating factor but I would like to know how to find it by adding the PI and CF together)