Find the Wronskian?

Question

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

Answer: -4(t*cos(t)-sin(t))

Answer 1

fg' - f'g = t*(cos(t)-sin(t))

uv' - u'v

= (f+3g)(f-g)' - (f+3g)'(f-g)

= -(f+3g+3f-3g)g'+f'(f+3g-f+g)

= -4[fg' - f'g]

= -4(t*cos(t)-sin(t)) <==Answer