Final answer:
The Wronskian of the functions y1 = 8x and y2 = 3x is calculated by evaluating the determinant of a matrix formed by these functions and their derivatives, resulting in a Wronskian value of 0.
Step-by-step explanation:
To calculate the Wronskian of two functions, y1 = 8x and y2 = 3x, we need to evaluate the determinant of a 2x2 matrix composed of these functions and their derivatives with respect to x. The Wronskian is defined as:
W(y1,y2) =
| y1 y2 |
| y1' y2' |
First, we need to find the derivatives of y1 and y2:
- y1' = d(8x)/dx = 8
- y2' = d(3x)/dx = 3
Now, we can construct the matrix and calculate its determinant:
W(y1,y2) =
| 8x 3x |
| 8 3 | = 8x*3 - 3x*8 = 0
Therefore, the Wronskian of y1 and y2 is 0.