5
$\begingroup$

I'm using the method of undetermined coefficients to find a particular solution of:

$$y''+y'=xe^{-x}$$

Ostensibly, it seems that $y_p$ should take the form of $(Ax + B)e^{-x}$

At least that's the form that I think I've been taught. Problem is that it just doesn't work out for me. I get a value for A, but not for B... Am I choosing an incorrect yp form?

  • 3
    Try $(Ax^2 + Bx) e^{-x}$. In your guess the value of $B$ is irrelevant since $B e^{-x}$ is always a solution to the homogeneous equation.2011-07-11
  • 0
    thanks for the advice. Unfortunately, I'm still hitting a dead end when substituting yp" and yp' into y" and y', but I'm sure I'm just making an error at some point. Gonna keep trying!2011-07-11

5 Answers 5