Let y1 t y2 t2 1 and y3 t t2 Find the Wronskian Wy1y2y3

Let y1 = t, y2 = t2 - 1 and y3 = t + t2. Find the Wronskian W(y1,y2,y3) Are these functions are linearly independent?

Solution

ay1 + by2 + cy3 =0

a(t) + b(t^2-1) + c(t+t^2) = 0

b =0

c+b =0 => c=0

a+c=0 = > a =0

ay1 + by2 + cy3 =0

=> a=b=c=0

hence linearly independent