Question

i need help to solve this step by step. please someone show me how.
\[W[y_{1},y_{2},y_{3}]=?\]
\[y_{1}(x)=e^x, y_2(x)=\cos x, y_3(x)= \sin x\]

Answer 1

must find the determinant of the Wronskian matrix
detW=?

Answer 2

W[y1,y2,y3] =/= 0, all 3 solutions are linearly independent.

Answer 3

| y1 y2 y3 |
| y1' y2' y3' | and take the determinate
| y1''y2''y3'' |