To find W(y1, y2)(2), we need to calculate the Wronskian of the solutions y1 and y2 at t = 2.
The Wronskian of two functions is given by the determinant of a matrix. In this case, the functions y1 and y2 are the solutions to the differential equation t^2y'' + 4y' + (5 + t)y = 0.
Let's denote y1 = y1(t) and y2 = y2(t). The Wronskian W(y1, y2) is given by:
W(y1, y2) = | y1 y2 |
| y1' y2' |
To find the Wronskian at t = 2, we need to substitute t = 2 into the functions and their derivatives.
First, we need to find y1'(t) and y2'(t) by taking the derivatives of y1 and y2, respectively.
Next, substitute t = 2 into y1, y2, y1', and y2' to obtain the values:
y1(2), y2(2), y1'(2), y2'(2).
Finally, substitute these values into the Wronskian formula:
W(y1, y2)(2) = | y1(2) y2(2) |
| y1'(2) y2'(2) |
Remember to round the answer to two decimal places as specified.