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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
11 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] 

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All the best Akhil!!!

Regards,
Askiitians Experts
Priyansh Bajaj

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