# Math Help - homogeneous ODE

1. ## homogeneous ODE

How do we get the root values for y''''-4y'''+7y''-6y+2y=0..?
Is it done by long division and we need to assume that one of the root is always = 1 by trial and error?

2. Originally Posted by ashes
How do we get the root values for y''''-4y'''+7y''-6y+2y=0..?
Is it done by long division and we need to assume that one of the root is always = 1 by trial and error?
Trial and error. In fact, (x - 1)^2 is a factor. The remaining (quadratic) factor is x^2 - 2x + 2.