# 2nd ODE constant coeff, quick question

1. Feb 17, 2008

### rock.freak667

1. The problem statement, all variables and given/known data
Solve:
$$\frac{d^2y}{dx^2}+\frac{dy}{dx}=3x^2+2x+1$$

3. The attempt at a solution

Well the C.F. is $y=C_1e^{-x}$
the P.I. is of the form $y_{PI}=Ax^3+Bx^2+Cx+D$

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 $y_{PI}$ 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)

2. Feb 17, 2008

### John Creighto

The D is redundant since one of the solutions to the natural equation is a constant function.

Therefor the constant function is determined by the initial conditions rather then the forcing function.

3. Feb 17, 2008

### rock.freak667

Ah...thanks then,I thought I was really doing something wrong.