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..

Dear Akhil,

Solution:- The general solution of given eq. f(x) = f ''(x) is f(x) = Ae^x + 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) = Ae^x + 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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