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###### Vijay posted an Question
July 19, 2022 • 21:05 pm 30 points
• CSIR NET
• Mathematical Sciences

## 55. let u and v de two solution oft y + p) y + q) y -0 on [a, b]. let wu, v) denote the wronskian of u and then (a) w(u, v) vanishes at a pont x, la, bj u and v

55. Let u and v De two solution oft y + P) y + Q) y -0 on [a, b]. Let Wu, v) denote the wronskian of u and Then (A) W(u, v) vanishes at a pont X, la, bj u and v are linearly dependent. (B) W(u, v) vanishes identically on [a, b]. >u and v are linearly dependent. (C) W(u, v) does not vanish at any point on [a, b] but u and v are lincarly dependent. (D) None of these.

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• ##### Nav

if Wronskian of two function y1 and y2 are identically zero on domain then functions y1 and y2 are linearly dependent in B Wronskian of y1 and y2 are identically zero on [a,b] therefore functions y1 and y2 are linearly dependent

• ##### Pankaj dwivedi Best Answer

Check the answer if Wronskian of two solution is identically zero on domain then these two solutions are linearly dependent hands option B is correct

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