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Which of the following differential equa...

Which of the following differential equations has `y=c_(1)e^(x)+c_(2)e^(-x)` as the general solution ?

A

`(d^(2)y)/(dx^(2))+y=0`

B

`(d^(2)y)/(dx^(2))-y=0`

C

`(d^(2)y)/(dx^(2))+1=0`

D

`(d^(2)y)/(dx^(2))-1=0`

Text Solution

AI Generated Solution

To find the differential equation that has the general solution \( y = c_1 e^x + c_2 e^{-x} \), we will follow these steps: ### Step 1: Differentiate \( y \) with respect to \( x \) Given: \[ y = c_1 e^x + c_2 e^{-x} \] We differentiate \( y \) to find \( \frac{dy}{dx} \): ...
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