ConstantCoefficients

# ConstantCoefficients - Linear Eq’s With Constant...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Linear Eq’s With Constant Coefficients We still want to consider 2nd order linear equations of the form y 00 + p ( x ) y + q ( x ) y = 0 but now we will restrict our attention to the case where p ( x ) and q ( x ) are constant functions. We won’t lose anything by allowing a nonzero constant coefficient of y 00 as well, since we could always divide it back out. Thus we will consider equations of the form ay 00 + by + cy = 0 . From our previous theorem, we are guaranteed that this equation has a general solution of the form y ( x ) = c 1 y 1 ( x ) + c 2 y 2 ( x ) , provided that we can find two linearly independent solutions y 1 and y 2 (i.e. solutions whose Wronskian is nonzero). An Educated Guess Regarding the solutions y 1 and y 2 , we are left with no alternative but to try to make an educated guess. From that the equation ay 00 + by + cy = 0 we can make a few observations: (1) The functions y,y , and y 00 must be of a similar shape, since constant multiples of them add to zero. For example no multiple ofto zero....
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

ConstantCoefficients - Linear Eq’s With Constant...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online