Originally Posted by

**akshatha** 1)

If { Ø1(x), Ø2(x) } is one set of two linearly independent solution on a ≤ x ≤ b and { ψ1(x), ψ2(x) } be another set of two linearly independent solution, then show that there exists a constant c ≠ 0 such that

W[ ψ1(x), ψ2(x) ] = c[ Ø1, Ø2 ](x) for all a ≤ x ≤ b.

where W[] is wronskian.

2)

If one of the solution of the linear equation

(1-x) y'' + xy' - y=0,

is y1(x)=x; find the second solution y2(x) such that y1(x) and y2(x) are linearly independent on some interval L.