Given that y=c1e3t+c2e−3t a solution to the differential equation y′′−9y=0, where c1 and c2 are arbitrary constants, find a function y that satisfies the conditions: y′′−9y=0, y(0)=7, limt→+[infinity]y(t)=0. Give your answer as y=... .
implies that when , .
For the condition , as , .
In the expression for , as , the term containing vanishes. Hence,
Substituting for and in ,
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Mathematics, published 11.05.2023
Mathematics, published 23.03.2023