11.    Which of the following differential equations has y = c_1e^x + c_2e^{-x} as the general solution?

                (A)    \frac{d^2y}{dx^2} + y = 0

                (B)    \frac{d^2y}{dx^2} - y = 0

                (C)    \frac{d^2y}{dx^2} +1 = 0

                (D)    \frac{d^2y}{dx^2} -1 = 0

Answers (1)
G Gautam harsolia

Given general solution is
y = c_1e^x + c_2e^{-x}
Differentiate it  w.r.t  x
we will get
\frac{dy}{dx} = c_1e^x-c_2e^{-x}
Again, Differentiate it  w.r.t  x
\frac{d^2y}{dx^2} = c_1e^x+c_2e^{x}=y\\ \frac{d^2y}{dx^2} - y = 0
Therefore,  (B) is the correct answer

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