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f(X)=f ''(x) ie function is equal to second order diff of itself..and f(0)=2 and f'(0)=3 find the function,, pls help me out..

f(X)=f ''(x) ie function is equal to second order diff of itself..and f(0)=2 and f'(0)=3 find the function,,


pls help me out..

Grade:11

1 Answers

Priyansh Bajaj AskiitiansExpert-IITD
30 Points
13 years ago

Dear Akhil,

Solution:- The general solution of given eq. f(x) = f ''(x) is f(x) = Aex + Be-x; where A and B are real numbers. it is very standard and you can easily derive it.

From the given conditions, you can find A and B.

f(x) = Aex + Be-x

  f(0) = A +B = 2

and, f '(0) = A- B = 3

So, A = 2.5 and B = -0.5

f(x) = 2.5ex - 0.5e-x [Ans] 

Please feel free to post as many doubts on our discussion forum as you can. If you find any question
Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation.

All the best Akhil!!!

Regards,
Askiitians Experts
Priyansh Bajaj

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