Question

how to factor out e^x from Wronskian W(e^2x,e^x)?

Answer 1

e^(2x)= e^(x+x)=e^(x)*e^(x)
so w=e^(x)*(e^(x),1)

Answer 2

| e^(2x) e^(x) |
| 2e^(2x) e^(x) | = e^(3x) - 3^(3x) = -e^(3x)

e^(x) | e^(x) 1 | = e^(x) (0) - e^(x) = -e^(2x)
| e^(x) 0 |