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Akhilesh posted an Question
February 22, 2022 • 21:24 pm 30 points
  • IIT JAM
  • Mathematics (MA)

1- consider the equation (1) +ai(0)x () + az(t)=(t) = 0 (1) where al, a2 are continuous functions on the interval i and to e i . suppose that ai(t) is a solutio

1- Consider the equation (1) +ai(0)x () + az(t)=(t) = 0 (1) where al, a2 are continuous functions on the interval I and to E I . Suppose that ai(t) is a solution of cquation (1) such that zi(t) # 0 t. Thcn (i) show that there exists a solution r2(t) on I such that the wronskian W[#1(t), *2(t)] =1; (1i) find a2(t) in terms of ri(t) by solving differential equation r1ah-r1#2 = erp|- Jt, ai (s)ds|.

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