Find the differential equation of the family of curves `y=A e^(2x)+B e^(-2x)` , where A and B are arbitrary constants.

Explanation

To find the differential equation of the family of curves given by \( y = A e^{2x} + B e^{-2x} \), where \( A \) and \( B \) are arbitrary constants, we will follow these steps:

### Step 1: Differentiate the equation once
We start with the equation:
\[ y = A e^{2x} + B e^{-2x} \]
Now, we differentiate \( y \) with respect to \( x \):
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