Wronskian Equation for y1 and y2 with Initial Conditions

[Temp0]

Homework Statement

W(t) = W(y1, y2) find the Wronskian.

Equation for both y1 and y2: 81y'' + 90y' - 11y = 0

y1(0) = 1
y1'(0) = 0
Calculated y1: (1/12)e^(-11/9 t) + (11/12)e^(1/9 t)

y2(0) = 0
y2'(0) = 1
Calculated y2: (-3/4)e^(-11/9 t) + (3/4)e^(1/9 t)

Homework Equations

W(y1, y2) = |y1 y2 |
| y1' y2' |

The Attempt at a Solution

After calculating y1 and y2, I don't seem to be able to do this determinant calculation. Mostly because it just doesn't look right, plugging in those giant equations and taking the derivative of them. Am I missing something here? Thanks for any help in advance.

 

[LCKurtz]

Homework Statement

W(t) = W(y1, y2) find the Wronskian.
y1(0) = 1
y1'(0) = 0
Calculated y1: (1/12)e^(-11/9 t) + (11/12)e^(1/9 t)

y2(0) = 0
y2'(0) = 1
Calculated y2: (-3/4)e^(-11/9 t) + (3/4)e^(1/9 t)

Homework Equations

W(y1, y2) = |y1 y2 |
| y1' y2' |

The Attempt at a Solution

After calculating y1 and y2, I don't seem to be able to do this determinant calculation. Mostly because it just doesn't look right, plugging in those giant equations and taking the derivative of them. Am I missing something here? Thanks for any help in advance.

Well, you didn't show us where these solutions came from so we can't check whether they are correct. But I suspect the idea isn't to calculate it directly like that. Does your text talk about Abel's theorem? There is a special equation that the Wronskian satisfies that relates $W(0)$ and the coefficients of your DE.

 

[Temp0]

Sorry, I have it now, and I have heard a little about Abel's Theorum, I'll try to find more information on it, thanks.

Edit: I got it after abit of research on Abel's Theorum, thanks so much.