Calculating Wronskian for u and v: f+3g and f-g

[Success]

If the Wronskian of f and g is tcos(t)-sin(t), and if u=f+3g, v=f-g, find the Wronskian of u and v.

W=fg'-gf'
(f+3g)(f-g)'-(f+3g)'(f-g)
What's next?

 

[Mark44]

Do not delete the template when you post. It's there for a reason. I'll let it slide this time...

If the Wronskian of f and g is tcos(t)-sin(t), and if u=f+3g, v=f-g, find the Wronskian of u and v.

W=fg'-gf'
(f+3g)(f-g)'-(f+3g)'(f-g)
What's next?

You have fg' - gf' = tcos(t)-sin(t).

I would expand (f+3g)(f-g)'-(f+3g)'(f-g) to see what that does. (f - g)' is just f' - g', and similar for (f + 3g)'.

 

[LCKurtz]

It would be easier to use properties of determinants. For example, what is W(u+v,g) in general for any u and v in terms of simpler Wronskians.