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Rajat Jain posted an Question
June 02, 2020 • 22:46 pm
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50 points
50 points
- IIT JAM
- Mathematics (MA)
9 consider the initial value problem y'(t) = f(t) y(t), y(0) = 1 where f r r is continuous. then this initial value problem has (a) (b) (c) (d) infinitely many
9 Consider the initial value problem y'(t) = f(t) y(t), y(0) = 1 Where f R R is continuous. Then this initial value problem has (A) (B) (C) (D) infinitely many solutions for somef a unique solution in R no solution in R for somef a solution in an interval containing 0, but not on R for some f
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Priyadarshan Choursiya![best-answer]()
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i don't understand
please explain again
I give explanation why we able to find A0. in normal questions you see that by giving condition you find integral constant which is unique, similarly this A0 you find when you know f(X). here continuity of f(X) say that you function f(X) will be integrated or approximated so you can find A0 for the question
how A=A0 in your solution
at t=0, we have y=1, and the e^integral give something at t=0 which we say A=0.
this is the property of continuous function that integral of every continuous function is differentiable so continuous also so it take some value at t=0
but e^x is strictly and continuous so it take some value, we can say that we have atleast one solution. but no such option is there so this option is more appropriate
since it may be possible that integral of f(X) make such as it becomes give more than 1 value at t=0. so we have B0,C0,,,,. but exactly how many they are we can only predict when we know function. so we only say we have atleast one solution