Ordinary differential equations....

If { f1(x), f2(x) } is one set of two linearly independent solution on a<=x<=b and { g1(x), g2(x) } be another set of two linearly independent solution, then show that there exists a constant c not equal to 0 such that

W [ g1(x), g2(x) ] = c W [ f1, f2] (x)

for all a<=x<=b.

where,

W[] is wronskian, which is defined as

W [ f1(x), f2(x)]= f1 (x) * f2 ' (x) - f1' (x) * f2' (x)

(determinant involving f1, f2 and f1' , f2' )

f1 ' (x) is derivative of f1(x) i.e., d( f1(x))/dx