- #1

aY'' + ibY' = 0

and thought that it could be written as:

[a, ib; -1, 1]

Then the determinant of this matrix would give the form

a + ib = 0

Is this correct and logically sound?

Thanks!

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- #1

aY'' + ibY' = 0

and thought that it could be written as:

[a, ib; -1, 1]

Then the determinant of this matrix would give the form

a + ib = 0

Is this correct and logically sound?

Thanks!

- #2

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- #3

eys_physics

- 268

- 72

aY'' + ibY' = 0

and thought that it could be written as:

[a, ib; -1, 1]

Then the determinant of this matrix would give the form

a + ib = 0

Is this correct and logically sound?

Thanks!

Hey, SeM,

I don't understand how you arrive at the second row in the matrix. Maybe, what you want to convert the second order differential equation into a system of two differential equations. This can be done by introducing

$$W(x)=Y'(x),$$

leading to the equations

$$aW'(x)+ibW(x)=0, \quad Y'(x)=W(x)$$

Indeed, both of your equations, i.e.

$$aY''(x)+ibY'(x)=0, Y''(x)-Y'(x)=0$$

if

$$a+ib=0,$$ but this is only a special case and it doesn't follow from your stated differential equation.

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